Mathematical Analysis and Numerical Methods

Missing data is a quite common issue in any dataset. Because the impact of missing data is substantial, several attempts have been done to produce methods to estimate the missing value. There is more than one classification for the missing imputation method; one is based on the imputation for continuous or categorical data. However, sometimes difficult to decide the best method the researcher should use due to the characteristics of the data, such as count. In this study, we evaluated two imputation methods to estimate the incomplete value in count data: Predictive Mean Matching (PMM), which is usually used for continuous data, and Multinomial Logistic Regression (MLR), a method used for categorical data. MLR showed AIC more close to the AIC of the original data; nevertheless, both methods maintained the original distribution of the data with tiny uncertainty. Further, neither did affect the selection of the best model that could fit the data better. More precisely, HZINB is the best count model fitting the original data and still outperforms the other count models after imputing the missing data using PMM and MLR.

In this work, we provide new scalar and matrix inequalities that include the difference between the Heinz mean and the arithmetic mean. In specifically, we obtain the inequality. $$\left( {\frac{{\text{p}}}{{\text{q}}}} \right)\left( {{\text{X}}\nabla {\text{Y}} - {\text{H}}_{{\text{q}}} \left( {{\text{X}},{\text{Y}}} \right)} \right) \le {\text{X}}\nabla {\text{Y}} - {\text{H}}_{{\text{p}}} \left( {{\text{X}},{\text{Y}}} \right) \le \left( {\frac{{1 - {\text{p}}}}{{1 - {\text{q}}}}} \right)\left( {{\text{X}}\nabla {\text{Y}} - {\text{H}}_{{\text{q}}} \left( {{\text{X}},{\text{Y}}} \right)} \right)$$ p q X ∇ Y - H q X , Y ≤ X ∇ Y - H p X , Y ≤ 1 - p 1 - q X ∇ Y - H q X , Y .for any $${\text{n}} \times {\text{n }}$$ n × n complex positive definite matrices $${\text{X}}$$ X and $${\text{ Y}}$$ Y , where $${\text{ X}} < {\text{Y}}$$ X < Y and $$0 < {\text{p}} \le {\text{q}} < 1$$ 0 < p ≤ q < 1 . Additionally, several determinant inequalities relevant to the Heinz and arithmetic means are given.

Researchers are becoming increasingly interested in using Fractional Partial Differential Equation (FPDE) models for physical systems such as gas flows through porous materials. These models rely on the fraction of the differentiation $$\alpha $$ α , which needs to be estimated from empirical data. Experimentation is needed to obtain empirical data where pressures need to be measured at various times, t, from the initial pressure and distances x from the pressure source which produces an output pressure p(x, t). While sampling times are easy to choose when a sensor is in place. Typically the location of sensors from the pressure source are arbitrarily chosen. This work shows how to design experiments using a two stage design with a base design and a follow design using D-optimality to determine the location(s) of additional sensors along x which allows for the minimization of the volume of the Variance-Covariance matrix of the parameters. A Bayesian approach is utilized for parameter estimation and simulated annealing is used to search through the possible locations for sensors in the follow up design. A simple FPDE is used to illustrate the approach with a base design of six sensor locations and follow-up designs for the simultaneous addition of 1, 2, 3, 4 and 5 new sensor locations. All of the follow-up designs suggest points near where the solution to the FPDE are optimal locations as well as other locations depending the number of sensors.

In the present work, we introduce a new subclasses of analytic functions with negative coefficients, using a differential operator involving q-Ruscheweyh Operator. We obtain the sufficient conditions and show some properties of functions belong to these subclasses: partial sums of its sequence and the q-neighborhoods problem are solved. Future research can focus on the symmetry properties and other properties of the subclass of functions introduced in this paper.

With the aid of Weiner’s group theoretic approach, the primary goal of this study is to investigate new intriguing generating relations for the harmonic oscillator-like functions. Also covered are unique instances of both recent and well-known results.

Comparisons among some new types of weighted mixed regression estimators for the linear regression model under the stochastic linear restrictions have been made in this paper. The mean squared error criterion is used to examine the superiority of different weighted mixed regression estimators. A Monte Carlo simulation study and real-life application are carried out to compare the performance of these estimators for different cases. Finally, we suggest the best weighted mixed regression estimator with collinear regressors.

In this work, Complex Sadik transform was applied to solving differential equations of the second kind as Volterra's integral equations. Several numerical applications were implemented that showed and interpreted the conversion. The obtained results confirmed that this conversion gave accurate results using the least arithmetic functions.

The exponential regression model is one of the most important and famous non-linear regression models. It is widely used in many experimental applications. This paper used the concept of weighted distributions to propose a modified exponential distribution and derive new regression model. Accordingly, two new weight probability density functions based on Renyi entropy were proposed: the Entropy-Based Weighted Exponential Distribution (EB-WE) and Renyi Entropy-Based Weighted Exponential Distribution (REB-WED). In this context, we derived the statistical characteristics for REB-WED, including the moment measures such as the population mean and r-th moment. Also, the measures of variation including the variance, standard deviation and coefficient of variation are proposed. Moreover, the measures of shape (i.e., skewness, kurtosis) and reliability measures included the hazard function, the odd function and reliability function also discussed. The unknown parameters of all proposed distributions were estimated by using the maximum likelihood estimation method. Also, the regression models are derived and its performances are discussed thru a Monte Carlo simulation experiments using the mean squared error and the bias criterions. The simulation results and the real data analyses indicated that the REB-WE regression model is more accurate and more efficient than the EB-WE regression model.

The most useful extension for fuzzy soft groups is the effective fuzzy soft group, which explains the effect of external efficacy on soft groups and is called effective fuzzy soft set (EFSS). This extension is the first extension of fuzzy soft set which considers the external effect on fuzzy soft set. Another extension of the fuzzy soft set was the time fuzzy soft set (TFSS) introduced by Ayman A. Hazaymeh in his Ph.D. thesis. In this paper we define the concept of effective time fuzzy soft set with respect time (ETFSS), which is the combination between effective fuzzy soft set and time fuzzy soft set. Also, we introduce basic operations and some properties of (ETFSS) with suitable examples.

In this work, one of the top new method called “Atomic Solution” that used to solve some partial fractional deferential equations that contains tensor product and variables from Banach space. This method is then used to solve the Fractional PDE Equation step by step, in order to illustrate the effectiveness of the method.

In this paper, we define new types of continuous functions in hereditary bi m-space namely $$(m_1,m_2)\text {-}\mathcal {H^*}_g$$ ( m 1 , m 2 ) - H ∗ g -continuous function and $$(m_1,m_2)\text {-}\mathcal {H}_g$$ ( m 1 , m 2 ) - H g -continuous function, we give some equivalent statements concerning these functions. Also we use these functions to introduce separation axioms and prove some related results.

In this paper, we continue to study the linear complexity of new generalized cyclotomic sequences. The generalized cyclotomic classes modulo $$p^nq^m$$ p n q m are used for the definition of these quaternary sequences. We develop the results obtained earlier for binary sequences and show that sequences under consideration have a high linear complexity.

This paper explores the structural measurement error model under the assumption of non-normal distribution for the error terms, specifically following the Exponential distribution. The article considers the use of non-identical distributions for the error terms and employs the Method of Moments (MOM) to estimate the unknown parameters based on these pre-assumptions. Real data on the relationships between Man-Hours and Workload are utilized to evaluate the performance of the estimators. Additionally, the precision of the estimators is compared with Wald-type grouping estimators. The findings of the analysis reveal that the grouping methods outperform the MOM in terms of fitting the non-normal structural measurement error model, as evidenced by lower mean squared error (MSE).

In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present a self-contained proofs for all of them, using a uniform terminology and technique. We illustrate their usefulness by providing several applications.

Due to the growing concern of intrusion and security threats, various measures have been implemented to safeguard valuable assets, data, and information. Among these measures, the Internet of Things (IoT) has emerged as a key technology in improving efficiency across multiple domains. This study aims to develop a mobile application with an autonomous system that can not only record footage from security cameras but also provide real-time alerts when someone enters a protected area. These alerts will be communicated via mobile notifications that will be prompt and easy to understand, allowing the owner to take necessary actions. The IoT technology will be used as a communication method between the system and the application, enabling seamless transfer of information over the internet. The system consists of two key elements: a mobile application developed in Java and face recognition software developed in Python using the OpenCV package and Haarcascade-frontalface-default model to identify faces in images and videos captured by the security cameras. The main contribution of this research is to minimize the need for extensive computations and comparisons while accurately identifying individuals through facial recognition.

Stress is a natural reaction to challenges encountered in everyday life. Chronic stress, which lasts for a long time, can negatively influence mental and physical health. Therefore, early detection and assessment of stress are crucial to reducing the risk of harm to an individual’s well-being. Electroencephalograph (EEG) brain signals can be used to assess human stress levels. This research aims to investigate how EEG signals can detect stress using deep learning based on a new feature extraction technique. We proposed new feature decomposition approaches based on the progressive Fourier transform and the coordination of multiple brain areas working simultaneously. Convolutional neural networks (CNNs) were employed in our study to extract and classify stress features captured from the image representations of EEG signals. The performance of the proposed method was evaluated on publicly available EEG dataset. Our experiment results demonstrated that our proposed method outperformed previous studies in detecting different mental states. The progressive Fourier transformation yielded the highest accuracy of 97.9% in classifying three mental states (Concentrating/Neutral/Relaxed) when conducting tenfolds cross validation using the AlexNet model.

The double ARA-Formable transform is a novel double integral transform that we present in this research. Existence conditions, partial derivatives, the double convolution theorem, with other properties and theorems are discussed. Moreover, we solve linear partial integro-differential equations (PIDE) using a convolution kernel and the double ARA-Formable transform. We solve a significant number of examples and show that the double ARA-Formable transform converts the PIDE into a solvable algebraic equation.

The double Laplace-Formable transform is a novel double integral transform that we present in this research. A number of partial derivatives, existence conditions, the theorem of double convolution, with other properties and theorems are discussed. Moreover, we investigate the solutions of some partial integro-differential equations by utilizing a convolution kernel, and the double Laplace-Formable transform. We solve a significant number of examples and show that the double Laplace-Formable transform converts the partial integro-differential equation into a solvable algebraic equation.

The Particle Swarm Optimization (PSO) algorithm is a well-known nature-inspired technique used to tackle complex optimization problems, widely used by researchers and practitioners due to its simplicity and effectiveness. This paper introduces an improved version of PSO, called Particle Swarm Optimization-based Variables Decomposition Method (PSO-VDM), which utilizes a decomposition technique and a semi-random initialization strategy to divide the problem into subproblems, enhancing exploration and exploitation of the search space. To evaluate the proposed algorithm, a comparison with seven other well-known algorithms is conducted across 13 benchmark problems. The search performance of the algorithms is analyzed using both the test of Wilcoxon signed-rank and Friedman rank. The results of the comparisons and statistical analyses demonstrate that the strategies employed in the PSO-VDM algorithm make a significant contribution to the search process. These comparisons indicate that the PSO-VDM algorithm outperforms other state-of-the-art optimization algorithms in terms of solution quality, highlighting its potential to effectively tackle challenging optimization problems.

Leishmaniasis, a complex disease, necessitates comprehensive research for a better understanding. Mathematical modeling can significantly enhance the precision of epidemiological studies and offer valuable insights. In this study, we employ classical derivatives and empirical data from Sudan to explore a conventional leishmaniasis model. However, our primary objective is to propose an innovative mathematical model for influenza, utilizing the Caputo fractional-order derivative operator instead of the standard operator. To compare the two models, we conduct numerical analyses that emphasize the dynamics of the influenza model, using the fractional Adams–Bashforth method. Additionally, we analyze the stability of the suggested dynamical model at disease-free and endemic equilibrium points, representing significant extremes in the model. These findings illuminate the potential of fractional calculus in effectively addressing epidemic threats.

In cases of emergency evacuation, the spread of fire inside buildings threatens evacuation routes, which in turn affects the evaluation process of evacuees to choose the appropriate exit. Providing the simulated evacuees with the capabilities of estimating fire propagation risk is essential for optimal decision making in evacuation simulation. In this article, for a more realistic evacuation simulation, the impact of risk from a threat source on exit selection behavior is taken into account. The simulated evacuees are provided with the ability to estimate the risk of alternative routes by providing a risk factor model. In addition, protection of agent from direct exposure to the threat is presented through modeling the precautionary time factor, based on maintaining a dynamically varying minimum distance with respect to agent safety. Simulations are performed to calibrate the parameters in the risk and precautionary time models. The effect of contribution on the evacuation process is investigated. Using the proposed model in order to test different configurations can enable researchers in the field of fire safety to provide an optimal building profile and to develop better guidance systems. In addition, it enhances the ability of simulation models to include more possibilities for interactions to examine the behavior of other evacuees.

In this paper, we introduce a new subclass of analytic functions defined on the symmetry domain $$\nabla $$ . The subclass is characterized by a derivative operator associated with quantum calculus. We obtain estimations for the Fekete-Szegö functional problems and for the absolute values of the second and third Taylor-Maclaurin coefficients of functions belonging to this new subclass. Additionally, we derive exact upper bounds for the second Hankel functional.

This research article effectively demonstrates the implementation of the modified Adomian decomposition method (MADM). Using a numerical procedure called MADM, some classes of Volterra integro differential equations can be solved can be solved with easily computational and high degree of acuracy. The procedure relies on ADM approximate series solutions, Laplace transform, and Pade approximants. The efficacy and dependability of MADM is tested through a numerical example. The results acquired reveal that the provided approach is highly effective and robust in addressing this differential equation.

In this study, we introduce a new class of bi-univalent functions constructed using $$q$$ q -Gegenbauer polynomials. We analyze and characterize this newly defined class of functions, and derive estimates for the Taylor-Maclaurin coefficients $$|a_{2}|$$ | a 2 | and $$|a_{3}|$$ | a 3 | . Additionally, we investigate the formulation of functional problems specific to functions within this subclass, namely $$\left| a_{3}-\sigma a_{2}^{2}\right| $$ a 3 - σ a 2 2 (commonly known as the Fekete-Szegö problem). By systematically exploring parameter specialization, we discover a range of novel outcomes that shed light on various aspects of our main results, contributing to a broader understanding of the mathematical landscape under investigation.

This paper investigates using Collatz Conjecture as a cryptographic algorithm to address the increasing demand for secure information and data access. The proposed encryption method utilizes a hash function inspired by the Collatz Conjecture to achieve significant randomization while maintaining the input’s integrity. The encryption scheme recursively adds the hash function’s output to the neighbouring pixel value, resulting in a highly secure encryption process. Several metrics were used to evaluate the proposed method’s performance, and the findings show that it outperforms existing encryption algorithms regarding data protection and computational speed. The proposed approach was evaluated using a range of established metrics, including but not limited to encryption and decryption speed, memory usage, and resistance to attacks. The Collatz Conjecture provides a means to generate pseudo-random numbers that can serve as keys for encryption, offering a novel approach to encryption that can withstand new hacking techniques and technological advancements. In addition to addressing the need for secure data access, the proposed encryption method has applications in various fields, including medical and military imaging, where data privacy and security are crucial. The findings of this paper provide valuable insights into the potential of the Collatz Conjecture as a new cryptographic algorithm and contribute to the development of encryption techniques that can ensure secure communication and protect sensitive data.

The main purpose of this study is introducing a novel generalization of some single integral transforms. The new double hybrid transform combines the Mellin and ARA transforms. We present the definition of the new transform, and investigate the basic properties such as the existence, the inverse and related theorems. New results on partially derivatives and the theorem of double convolution are introduced and discussed.

Let $$f(z)=z+\sum _{k=n}^{\infty }a_k z^k;(n\ge 2)$$ f ( z ) = z + ∑ k = n ∞ a k z k ; ( n ≥ 2 ) be a bi-univalent function in the unit disk $$\mathbb {U}=\{z:\;|z|<1\})$$ U = { z : | z | < 1 } ) . We investigate bounds of $$|a_{n}|$$ | a n | , $$|a_{2n-1}|$$ | a 2 n - 1 | , $$|a_{2n-1}-na_n^2|$$ | a 2 n - 1 - n a n 2 | and $$|a_{2n-1}-a_n^2|$$ | a 2 n - 1 - a n 2 | for classes of bi-univalent functions defined by fractional derivatives. The results include generalizations and improvements for well known estimates.

In this paper, new types of upper and lower bounds for generalized of logarithmic and identric means are constructed based on novel relations between scalar means and hyperbolic functions.

This paper introduces a novel analytic approach for solving Dirichlet boundary-value problems for regular solutions of second-order elliptic differential equations. The methodology uses complex variables $$z=x+iy$$ z = x + i y and $$\zeta =x-iy$$ ζ = x - i y and integral representation techniques for regular solutions within the multiply connected domain $$T$$ T . The regular solution is represented as $$\text{Re} U(z, \zeta )$$ Re U ( z , ζ ) satisfying the symmetry condition $$U(\overline{\zeta }, \overline{z } ) = \stackrel{-}{(U(z, \zeta ))}$$ U ( ζ ¯ , z ¯ ) = ( U ( z , ζ ) ) - . This approach extends its applicability beyond domains bounded by Lyapunov and Vekua and provides efficient resolutions for Dirichlet boundary-value problems in multiply connected domains for real elliptic equations.

This article aims to introduce Structural Measurement Error Models (SMEM) in the context of big data analytics. The maximum likelihood estimation method was implemented to estimate unknown parameters and fit data to the suggested models. The performance of fitting big data using a sub-sampling algorithm was evaluated based on several criteria including the program execution time, bias, mean squared error of estimators, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). R software was used to conduct Monte Carlo simulation experiments. Then the research idea was implemented on real data to analyze the relationship between the number of passengers and population size, based on a sample of one million passengers. Both simulation experiments and real data analysis revealed that dividing data into several groups improved machine performance in terms of time but with less informative results in terms of AIC and BIC.

This paper aims to present a numerical solution to the fractional stochastic population growth model equation by using modified three-point fractional formula. Such a formula, which can be derived from the generalized Taylor theorem, is used to approximate Riemann-Liouville fractional integral operator. To show the effectiveness of the numerical method, the approximate solution is compared with the exact solution coupled with the approximate solution generated from the Euler-Maruyama method. Finally, the results of numerical experiments are supported with graphs for completeness.

An analytical solution is proposed in this work for the non-linear time-fractional Zakharov-Kuznetsov partial differential equation (FZK-PDE) in the Caputo sense. The FZK-PDE model demonstrates the behavior of weakly nonlinear ion-acoustic waves in a plasma with a uniform magnetic field. A series solution for the FZK-PDE is obtained using the so-called Laplace-Residual power series method (L-RPSM). The L-RPSM is a simple and efficient technique for obtaining approximate and exact series solution of nonlinear and linear fractional differential equations (FDEs). Graphical and numerical solutions of several test examples show the reliability and efficiency of the L-RPSM. Moreover, the results show that the L-RPSM is powerful, competitive, simple, and reliable for a wide range of fractional PDEs.

Recommendation plays a crucial part in our digital life. When there are no recommendations, getting disoriented in a sea of data is accessible. In massive data sets, the recommendation system (RS) has proven to be an effective information filtering tool, minimizing the information overload experienced by Web users. Collaborative filtering (CF) provides recommendations to the currently active user without first reviewing the content of the information resource. These suggestions or recommendations are based on a lot of user history data. In recent years, it has been seen a decline in the performance of collaborative filtering-based recommendation systems due to a need for more data and a large amount of information. Movies or films, as highly significant entertainment, are usually suggested and endorsed to us by other people. Each individual enjoys a specific kind or sub-genre of film. Most websites like Netflix and IMDB are operating based on recommendations. The only issue that may fail the recommendation system is the difficulty caused by sparsity. In this paper, a new approach will be discussed that has the potential to tackle the problem of sparsity.

The goal of this work is to evaluate the impact of hybrid nanofluids’ chaotic fractional-order behavior in a fluid layer that is heated from below. Ag–Cu/Water; Al2O3–Cu/Water hybrid nanofluids are used. The fractional nonlinear system is solved using the method of Adams-Bashforth-Moulton. Numerical simulations are provided to demonstrate the effectiveness. The findings demonstrate that fractional-order can be used to investigate the inhibition of chaotic convection when hybrid nanofluids are used.

In this article, we establish several inequalities for the generalized numerical radius of $$2\times 2$$ 2 × 2 block matrices. Furthermore, we introduce innovative improvements to the generalized numerical radius inequalities for matrix sums and products.

In this study, we introduce the new double formable transform for solving fractional partial differential equations. The basic theorems and properties of the double formable transform are presented and discussed. Moreover, new formulas that illustrate the applications of the double Formable transform to some fractional operators are introduced and proved. We solve some examples of fractional partial differential equations, and show the simplicity of using the new approach in solving examples.

In this research, we present a new numerical method for solving fractional partial differential equations. This new approach is based on the combination of the general transformation and decomposition method. The general transform is a new integral transform that generalizes most of the Laplace transforms. In this study, it is combined with the decomposition technique to solve the time-fractional Klein-Gordon equation (TFKGE). The solution is presented in the form of a comprehensive analytical series expansion. Additionally, we provide a thorough analysis of numerical examples that effectively highlight the robustness and efficacy of the proposed method.

In more recent years, the number of cases of monkeypox illness has progressively risen, and the anticipated geographic scope of outbreaks in human populations have expanded as well. This work suggests a novel fractional-order variant of one of the Susceptible-Exposed-Infectious-Recovered models in light of these factors (or SEIR models). To discover certain theoretical findings about the fundamental reproduction number, this model, which is formulated in the sense of a Caputo fractional differentiator, is first examined. The suggested model is then numerically solved using a fresh, modern variation of the fractional Euler approach known as Improved Modified Fractional Euler Method 1 and 2 (IMFEM1, IMFEM2). For completeness, more numerical simulations are provided after that.

With the evolution of many studies of heat transfer characteristics that are enhanced by suspended nanoparticles in the based fluids, these studies have gradually become a significant topic in the area of mechanical engineering and new industrial domains. Especially, the problems of the convection boundary layer flow of incompressible nanofluids have received a lot of important studies. Wherefore, there is still a need for studies that enhance the properties of heat transfer in the based fluids. The current study objective is numerically to investigate the characteristics of heat and mass transfer over a stretching sheet in Casson Ternary Hybrid nanofluids, under a magnetic field, with constant wall temperature boundary conditions. Using suitable similarity transformations, the governing equations are reduced to a set of partial differential equations. The Keller-Box technique is used to solve partial differential equations that have been transformed into a linear system of equations. MATLAB program codes are utilized to present the numerical results of studied physical quantities. The impacts of Casson, nanoparticles volume fractions, and magnetic parameters, on the physical quantities, namely Nusselt number, skin friction, velocity, and temperature are examined and shown as graphs and tables. The research shows that an increase in the Casson parameter and the magnetic parameter causes an improvement in the thermal boundary layer, hence decreasing the fluid velocity and skin friction coefficient. Compared to the prior findings, the accuracy of the present results has significantly agreed.

Multiple Linear Regression is a form of analysis or technique that shows how a continuous dependent variable is related to two or more independent variables. It plays a significant role in the general linear model. When two or more predictor variables are associated, a challenge is always encountered in the use of Multiple Linear Regression. This challenge is called Multicollinearity that can inflate the Least Squares Regression Coefficient estimates, which are dependent on the correlated predictor variables in the model. Researchers in several fields such as Finance and Economics have been faced with this unavoidable difficulty. Multicollinearity can cause inaccurate coefficient variances and unstable estimates, making it harder to decide the fit model. Hence, to address multicollinearity, alternative modalities like Ridge Regression have been offered. The value of the Ridge Parameter k, as scalar, vector, and matrix, can be calculated in different ways. This paper tries to determine the optimal Ridge Parameter as per the mean squares error criterion.

This study aims to investigate the relationship between hypertension and diabetes, two chronic diseases with significant public health implications. While the association between these two diseases has been well-established, the underlying pathogenic mechanisms remain unclear. The authors propose to use a recently developed model for studying multimorbidity, which considers the interactions between risk factors for each disease. We use a coupled hidden Markov model (CHMM) with binomial and truncated geometric copulas to analyze hospital appointment data from a private hospital between January 2015 and December 2020. The results suggest that the CHMM with discrete copulas is an effective tool for examining disease multimorbidity, particularly when clinical data is scarce. The study contributes to our understanding of the complex relationship between hypertension and diabetes, and highlights the importance of considering the interdependence of risk factors in the development of chronic diseases.

Glioblastoma, also known as glioblastoma multiforme (GBM), is the most deadly cancer that infects the brain. Cancer is one of the most vicious killers in the world and the control of tumor growth requires special attention. The typical approach for treating GBM involves surgical resection of as much of the tumor as possible. This paper aims to present a numerical solution for a recent fractional-order model connected with glioblastoma multiforme. This will be done by employing a recent numerical scheme called the Modified Fractional Euler Method (MFEM). Some numerical comparisons will be performed between our proposed scheme and the traditional numerical scheme; Fractional Euler Method (FEM).