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Numerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernels

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dc.contributor.author Alomari, Abedel-Karrem
dc.contributor.author Abdeljawad, Thabet
dc.contributor.author Baleanu, Dumitru
dc.contributor.author Saad, Khaled M.
dc.contributor.author Al-Mdallal, Qasem M.
dc.date.accessioned 2022-08-29T11:51:10Z
dc.date.available 2022-08-29T11:51:10Z
dc.date.issued 2020
dc.identifier.citation Alomari, Abedel-Karrem...et al. (2020). "Numerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernels", Numerical Methods for Partial Differential Equations. tr_TR
dc.identifier.issn 0749-159X
dc.identifier.uri http://hdl.handle.net/20.500.12416/5781
dc.description.abstract In this article, we investigate the generalized fractional operator Caputo type (ABC) with kernels of Mittag–Lefller in three parameters Eα,µγ(λ,t) and its fractional integrals with arbitrary order for solving the time fractional parabolic nonlinear equation. The generalized definition generates infinitely many problems for a fixed fractional derivative α. We utilize this operator with homotopy analysis method for constructing the new scheme for generating successive approximations. This procedure is used successfully on two examples for finding the solutions. The effectiveness and accuracy are verified by clarifying the convergence region in the ℏ-curves as well as by calculating the residual error and the results were accurate. Based on the experiment, we verify the existence of the solution for the new parameters. Depending on these results, this treatment can be used to find approximate solutions to many fractional differential equations. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.1002/num.22699 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Homotopy Analysis Method tr_TR
dc.subject Mittag–Lefller Kernel tr_TR
dc.subject Time Fractional Parabolic Nonlinear Equation tr_TR
dc.title Numerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernels tr_TR
dc.type article tr_TR
dc.relation.journal Numerical Methods for Partial Differential Equations tr_TR
dc.contributor.authorID 56389 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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