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22-01-2020 | Methodologies and Application

Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions

Authors: Omar Abu Arqub, Mohammed Al-Smadi

Published in: Soft Computing | Issue 16/2020

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Abstract

The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called fuzzy conformable. To this end, we discussed fuzzy conformable fractional integral softly. Meanwhile, uniqueness, existence, and other properties of solutions of certain fuzzy conformable fractional differential equations under strongly generalized differentiability are also utilized. Furthermore, all needed requirements for characterizing solutions by equivalent systems of crisp conformable fractional differential equations are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate conformable solutions are proposed. Finally, the reproducing kernel Hilbert space method in the conformable emotion is constructed side by side with numerical results, tabulated data, and graphical representations.

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Abdeljawad T (2015) On conformable fractional calculus. J Comput Appl Math 279:57–66MathSciNetMATH

Abu Arqub O (2016a) The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations. Math Methods Appl Sci 39:4549–4562MathSciNetMATH

Abu Arqub O (2016b) Approximate solutions of DASs with nonclassical boundary conditions using novel reproducing kernel algorithm. Fundam Informat 146:231–254MathSciNetMATH

Abu Arqub O (2017a) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations. Neural Comput Appl 28:1591–1610

Abu Arqub O (2017b) Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions. Comput Math Appl 73:1243–1261MathSciNetMATH

Abu Arqub O (2018a) Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm. Int J Numer Meth Heat Fluid Flow 28:828–856

Abu Arqub O (2018b) Solutions of time-fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space. Numer Methods Partial Differ Equ 34:1759–1780MathSciNetMATH

Abu Arqub O (2018c) Numerical solutions of systems of first-order, two-point BVPs based on the reproducing kernel algorithm. Calcolo 55:1–28MathSciNetMATH

Abu Arqub O (2019a) Numerical simulation of time-fractional partial differential equations arising in fluid flows via reproducing Kernel method. Int J Numer Methods Heat Fluid Flow. https://doi.org/10.1108/HFF-10-2017-0394 CrossRef

Abu Arqub O (2019b) Numerical algorithm for the solutions of fractional order systems of Dirichlet function types with comparative analysis. Fundam Informat 166:111–137MathSciNetMATH

Abu Arqub O, Al-Smadi M (2014) Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations. Appl Math Comput 243:911–922MathSciNetMATH

Abu Arqub O, Al-Smadi M (2018a) Atangana-Baleanu fractional approach to the solutions of Bagley-Torvik and Painlevé equations in Hilbert space. Chaos Solitons Fractals 117:161–167MathSciNet

Abu Arqub O, Al-Smadi M (2018b) Numerical algorithm for solving time-fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions. Numer Methods Partial Differ Equ 34:1577–1597MathSciNetMATH

Abu Arqub O, Al-Smadi M (2019) An adaptive numerical approach for the solutions of fractional advection–diffusion and dispersion equations in singular case under Riesz’s derivative operator. Statistical Mechanics and its Applications. In Press, Physica A. https://doi.org/10.1016/j.physa.2019.123257 CrossRef

Abu Arqub O, Maayah B (2018) Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana-Baleanu fractional operator. Chaos Solitons Fractals 117:117–124MathSciNet

Abu Arqub O, Maayah B (2019a) Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC–Fractional Volterra integro-differential equations. Chaos Solitons Fractals 126:394–402MathSciNet

Abu Arqub O, Maayah B (2019b) Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense. Chaos Solitons Fractals 125:163–170MathSciNet

Abu Arqub O, Shawagfeh N (2019a) Solving optimal control problems of Fredholm constraint optimality via the reproducing kernel Hilbert space method with error estimates and convergence analysis. Math Methods Appl Sci 2019:1–18. https://doi.org/10.1002/mma.5530 CrossRef

Abu Arqub O, Shawagfeh N (2019b) Application of reproducing kernel algorithm for solving Dirichlet time-fractional diffusion-Gordon types equations in porous media. J Porous Media 22:411–434

Abu Arqub O, Al-Smadi M, Shawagfeh N (2013) Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method. Appl Math Comput 219:8938–8948MathSciNetMATH

Abu Arqub O, Al-Smadi M, Momani S, Hayat T (2016) Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method. Soft Comput 20:3283–3302MATH

Abu Arqub O, Al-Smadi M, Momani S, Hayat T (2017) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 21:7191–7206MATH

Abu Arqub O, Odibat Z, Al-Smadi M (2018) Numerical solutions of time-fractional partial integrodifferential equations of Robin functions types in Hilbert space with error bounds and error estimates. Nonlinear Dyn 94:1819–1834MATH

Akgül A (2018) A novel method for a fractional derivative with non-local and non-singular kernel. Chaos Solitons Fractals 114:478–482MathSciNetMATH

Al-Smadi M, Abu Arqub O (2019) Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates. Appl Math Comput 342:280–294MathSciNetMATH

Bede B, Gal SG (2005) Generalizations of the differentiability of fuzzy number value functions with applications to fuzzy differential equations. Fuzzy Sets Syst 151:581–599MATH

Berlinet A, Agnan CT (2004) Reproducing kernel Hilbert space in probability and statistics. Kluwer Academic Publishers, USAMATH

Chalco-Cano Y, Román-Flores H (2008) On new solutions of fuzzy differential equations. Chaos Solitons Fractals 38:112–119MathSciNetMATH

Chen C, Jiang Y (2018) Simplest equation method for some time-fractional partial differential equations with conformable derivative. Comput Math Appl 75:2978–2988MathSciNetMATH

Cui M, Lin Y (2009) Nonlinear numerical analysis in the reproducing kernel space. Nova Science, USAMATH

Daniel A (2003) Reproducing kernel spaces and applications. Springer, Basel, SwitzerlandMATH

Deng W, Zhao H, Yang X, Xiong J, Sun M, Li B (2017a) Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl Soft Comput 59:288–302

Deng W, Zhao H, Zou L, Li G, Yang X, Wu D (2017b) A novel collaborative optimization algorithm in solving complex optimization problems. Soft Comput 21:4387–4398

Deng W, Xu J, Zhao H (2019) An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem. I\epsilon Access 7:20281–20292

Fedorchenko AI (2008) Introduction to fractional calculus. Czech Republic. https://doi.org/10.13140/2.1.1890.6887 CrossRef

Geng FZ, Qian SP, Li S (2014) A numerical method for singularly perturbed turning point problems with an interior layer. J Comput Appl Math 255:97–105MathSciNetMATH

Goetschel R, Voxman W (1986) Elementary fuzzy calculus. Fuzzy Sets Syst 18:31–43MathSciNetMATH

Herrmann R (2014) Fractional calculus: an introduction for physicists. World Scientific, SingaporeMATH

Jiang W, Chen Z (2014) A collocation method based on reproducing kernel for a modified anomalous subdiffusion equation. Numer Methods Partial Differ Equ 30:289–300MathSciNetMATH

Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24:301–317MathSciNetMATH

Khalil R, Horani M, Yousef A, Sababheh M (2014) A new definition of fractional derivative. Comput Appl Math 246:65–70MathSciNetMATH

Kilbas A, Srivastava H, Trujillo J (2006) Theory and applications of fractional differential equations. Elsevier, NetherlandsMATH

Kumar D, Seadawy A, Joardar A (2018) Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology. Chin J Phys 56:75–85

Lin Y, Cui M, Yang L (2006) Representation of the exact solution for a kind of nonlinear partial differential equations. Appl Math Lett 19:808–813MathSciNetMATH

Liu Y, Wang X, Zhai Z, Chen R, Zhang B, Jiang Y (2019) Timely daily activity recognition from headmost sensor events. ISA Trans 94:379–390

Puri ML (1986) Fuzzy random variables. J Math Anal Appl 114:409–422MathSciNetMATH

Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Sets Syst 24:319–330MathSciNetMATH

Senol M, Tasbozan O, Kurt A (2019) Numerical solutions of fractional Burgers’ type equations with conformable derivative. Chin J Phys 58:75–84

Tarasov VE (2011) Fractional dynamics: applications of fractional calculus to dynamics of particles, fields and media. Springer, Germany

Thabet H, Kendre S (2018) Analytical solutions for conformable space-time fractional partial differential equations via fractional differential transform. Chaos Solitons Fractals 109:238–245MathSciNetMATH

Ünal E, Gökdoğan A (2018) Solution of conformable fractional ordinary differential equations via differential transform method. Optik 128:264–273

West BJ (2017) Natures patterns and the fractional calculus. De Gruyter, Germany

Zhao H, Liu H, Xu J, Deng W (2019a) Performance prediction using high-order differential mathematical morphology gradient spectrum entropy and extreme learning machine. I\epsilon Trans Instrum Meas. https://doi.org/10.1109/tim.2019.2948414 CrossRef

Zhao H, Zheng J, Xu J, Deng W (2019b) Fault diagnosis method based on principal component analysis and broad learning system. I\epsilon Access 7:99263–99272

Zhoua Y, Cui M, Lin Y (2009) Numerical algorithm for parabolic problems with non-classical conditions. J Comput Appl Math 230:770–780MathSciNetMATH

Title: Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions
Authors: Omar Abu Arqub
Mohammed Al-Smadi
Publication date: 22-01-2020
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 16/2020
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-020-04687-0

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