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

dc.contributor.authorAlomari, Abedel-Karrem
dc.contributor.authorAbdeljawad, Thabet
dc.contributor.authorBaleanu, Dumitru
dc.contributor.authorSaad, Khaled M.
dc.contributor.authorAl-Mdallal, Qasem M.
dc.contributor.authorID56389tr_TR
dc.date.accessioned2022-08-29T11:51:10Z
dc.date.available2022-08-29T11:51:10Z
dc.date.issued2020
dc.departmentÇankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractIn 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.en_US
dc.identifier.citationAlomari, Abedel-Karrem...et al. (2020). "Numerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernels", Numerical Methods for Partial Differential Equations.en_US
dc.identifier.doi10.1002/num.22699
dc.identifier.issn0749-159X
dc.identifier.urihttp://hdl.handle.net/20.500.12416/5781
dc.language.isoenen_US
dc.relation.ispartofNumerical Methods for Partial Differential Equationsen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectHomotopy Analysis Methoden_US
dc.subjectMittag–Lefller Kernelen_US
dc.subjectTime Fractional Parabolic Nonlinear Equationen_US
dc.titleNumerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernelstr_TR
dc.titleNumerical Solutions of Fractional Parabolic Equations With Generalized Mittag–leffler Kernelsen_US
dc.typeArticleen_US
dspace.entity.typePublication

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