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2024 | OriginalPaper | Chapter

General Transform Decomposition Method

Authors : Rania Saadeh, Bayan Ghazal, Ahmad Qazza

Published in: Mathematical Analysis and Numerical Methods

Publisher: Springer Nature Singapore

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Abstract

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.

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previous chapter Using Double Formable Transform to Solve Fractional Partial Differential Equations
next chapter Solving Fractional-Order Monkeypox Model by New Numircal Methods
Literature
1.
Qazza, A., Hatamleh, R., Alodat, N.: About the solution stability of Volterra integral equation with random kernel. Far East J. Math. Sci. 100, 671–680 (2016)
2.
Gharib, G., Saadeh, R.: Reduction of the self-dual yang-mills equations to sinh-poisson equation and exact solutions. WSEAS Interact. Mathemat. 20, 540–554
3.
Qazza, A., Hatamleh, R.: The existence of a solution for semi-linear abstract differential equations with infinite B chains of the characteristic sheaf. Int. J. Appl. Math. 31, 611–620 (2018)CrossRef
4.
Saadeh, R., Al-Smadi, M., Gumah, G., Khalil, H., Khan, A.: Numerical investigation for solving two-point fuzzy boundary value problems by reproducing kernel approach. Appl. Math. Inform. Sci. 10(6), 1–13 (2016)MathSciNetCrossRef
5.
Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific Publishing Co. Inc., River Edge, NJ (2000)CrossRef
6.
Laroche, E., Knittel, D.: An improved linear fractional model for robustness analysis of a winding system. Control. Eng. Pract. 13, 659–666 (2005)CrossRef
7.
Lai, J., Liu, F., Anh, V., Liu, Q.: A space-time finite element method for solving linear Riesz space fractional partial differential equations. Numer. Algorithms 88(1), 499–520 (2021)MathSciNetCrossRef
8.
Calderon, A., Vinagre, B., Feliu, V.: Fractional order control strategies for power electronic buck converters. Signal Proc. 86, 2803–2819 (2006)CrossRef
9.
Saadeh, R.: Numerical algorithm to solve a coupled system of fractional order using a novel reproducing kernel method. Alex. Eng. J. 60(5), 4583–4591 (2021)CrossRef
10.
Monje, C., Vinagre, B., Feliu, V., Chen, Y.: Tuning and auto tuning of fractional order controllers for industry applications. Control. Eng. Pract. 16, 798–812 (2008)CrossRef
11.
Ahmed, S.A., Qazza, A., Saadeh, R.: Exact solutions of nonlinear partial differential equations via the new double integral transform combined with iterative method. Axioms 11(6), 247 (2022)CrossRef
12.
Edwan, R., Saadeh, R., Hadid, S., Al-Smadi, M., Momani, S.: Solving time-space-fractional cauchy problem with constant coefficients by finite-difference method. In: Zeidan, D., Padhi, S., Burqan, A., Ueberholz, P. (eds) Computational Mathematics and Applications. Forum for Interdisciplinary Mathematics. Springer, Singapore (2020)
13.
Liao, J.: The proposed homotopy analysis technique for the solution of nonlinear problems. School of Ship and Ocean Engineering, Shanghai Jiao Tong University, Shanghai, China, Ph.D. dissertation (1992)
14.
Saadeh, R., Ghazal, B.: A new approach on transforms: formable integral transform and its applications. Axioms 10(4), 332 (2021)CrossRef
15.
Saadeh, R., Qazza, A., Burqan, A.: A new integral transform: ARA transform and its properties and applications. Symmetry 12(6), 925 (2020)CrossRef
16.
Qazza, A., Burqan, A., Saadeh, R.: A new attractive method in solving families of fractional differential equations by a new transform. Mathematics 9(23), 3039 (2021)CrossRef
17.
Burqan, A., Saadeh, R., Qazza, A., Momani, S.: ARA-residual power series method for solving partial fractional differential equations. Alexandria Eng. J. (2022)
18.
Burqan, A., Saadeh, R., Qazza, A.: A novel numerical approach in solving fractional neutral pantograph equations via the ARA integral transform. Symmetry 14(1), 50 (2022)CrossRef
19.
Burqan, A., El-Ajou, A., Saadeh, R., Al-Smadi, M.: A new efficient technique using Laplace transforms and smooth expansions to construct a series solution to the time-fractional Navier-Stokes equations. Alex. Eng. J. 61(2), 1069–1077 (2022)CrossRef
20.
Saadeh, R.: A generalized approach of triple integral transforms and applications. J. Math. (2023)
21.
Prakasha, D.G., Saadeh, R., Kachhia, K., Qazza, A., Malagi, N.S.: A New Computational Technique for Analytic Treatment of Time-Fractional Nonlinear Equations Arising in Magneto-Acoustic Waves. Mathematical Problems in Engineering (2023)
22.
Saadeh, R., Sedeeg, A.K., Ghazal, B., Gharib, G.: Double formable integral transform for solving heat equations. Symmetry 15(1), 218 (2023)CrossRef
23.
Jafari, H.: A new general integral transform for solving integral equations. J. Adv. Res. 32, 133–138 (2021)CrossRef
24.
Guo, Y., Vazquez, L.: A numerical scheme for nonlinear Klein Gordon equations. J. Appl. Sci. 1, 25–32 (1983)
25.
26.
Adomian G.: Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Publishers (1994)
27.
Adomian, G.L.: Nonlinear Stochastic Operator Equations. Kluwer Academic Publishers (1986)
28.
Jafari, H.: Numerical solution of time-fractional Klein–Gordon equation by using the decomposition methods. J. Comp. Nonlinear Dyn. 11(4) (2016)
29.
Deeba, E., Khuri, S.: A decomposition method for solving the nonlinear Klein-Gordon equation. J. Comput. Phys. 124(2), 442–448 (1996)MathSciNetCrossRef
30.
El-Sayed, M.: The decomposition method for studying the Klein-Gordon equation. Chaos Solitons Fract. 18(5), 1025–1030 (2003)MathSciNetCrossRef
31.
Yusufo˘glu, E.: The variational iteration method for studying the Klein-Gordon equation. Appl. Math. Lett. 21(7), 669–674 (2008)
32.
Kumar, A., Baleanu, D.: An analysis for Klein-Gordon equation using fractional derivative having Mittag-Leffler-type kernel. Math. Methods Appl. Sci. 44(7), 5458–5474 (2021)MathSciNetCrossRef
Metadata
Title
General Transform Decomposition Method
Authors
Rania Saadeh
Bayan Ghazal
Ahmad Qazza
Copyright Year
2024
Publisher
Springer Nature Singapore
Book
Mathematical Analysis and Numerical Methods

Print ISBN: 978-981-9748-75-4

Electronic ISBN: 978-981-9748-76-1

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-981-97-4876-1_37

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