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Numerical solution of two-dimensional time fractional cable equation with Mittag-Leffler kernel

dc.contributor.authorKumar, Sachin
dc.contributor.authorBaleanu, Dumitru
dc.contributor.authorID56389tr_TR
dc.date.accessioned2021-01-08T12:47:39Z
dc.date.available2021-01-08T12:47:39Z
dc.date.issued2020
dc.departmentÇankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractThe main motive of this article is to study the recently developed Atangana-Baleanu Caputo (ABC) fractional operator that is obtained by replacing the classical singular kernel by Mittag-Leffler kernel in the definition of the fractional differential operator. We investigate a novel numerical method for the nonlinear two-dimensional cable equation in which time-fractional derivative is of Mittag-Leffler kernel type. First, we derive an approximation formula of the fractional-order ABC derivative of a function t(k) using a numerical integration scheme. Using this approximation formula and some properties of shifted Legendre polynomials, we derived the operational matrix of ABC derivative. In the author of knowledge, this operational matrix of ABC derivative is derived the first time. We have shown the efficiency of this newly derived operational matrix by taking one example. Then we solved a new class of fractional partial differential equations (FPDEs) by the implementation of this ABC operational matrix. The two-dimensional model of the time-fractional model of the cable equation is solved and investigated by this method. We have shown the effectiveness and validity of our proposed method by giving the solution of some numerical examples of the two-dimensional fractional cable equation. We compare our obtained numerical results with the analytical results, and we conclude that our proposed numerical method is feasible and the accuracy can be seen by error tables. We see that the accuracy is so good. This method will be very useful to investigate a different type of model that have Mittag-Leffler fractional derivative.en_US
dc.description.publishedMonth5
dc.identifier.citationKumar, Sachin; Baleanu, Dumitru (2020). "Numerical solution of two-dimensional time fractional cable equation with Mittag-Leffler kernel",Mathematical Methods in the Applied Sciences, Vol. 43, No. 15, pp. 8348-8362.en_US
dc.identifier.doi10.1002/mma.6491
dc.identifier.endpage8362en_US
dc.identifier.issn0170-4214
dc.identifier.issn1099-1476
dc.identifier.issue15en_US
dc.identifier.startpage8348en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/4465
dc.identifier.volume43en_US
dc.language.isoenen_US
dc.relation.ispartofMathematical Methods in the Applied Sciencesen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectCable Equationen_US
dc.subjectFractional Derivative With Mittag-Leffler Kernelen_US
dc.subjectLegendre Polynomialen_US
dc.subjectOperational Matrixen_US
dc.subjectTwo-Dimensional Fractional PDEen_US
dc.titleNumerical solution of two-dimensional time fractional cable equation with Mittag-Leffler kerneltr_TR
dc.titleNumerical Solution of Two-Dimensional Time Fractional Cable Equation With Mittag-Leffler Kernelen_US
dc.typeArticleen_US
dspace.entity.typePublication

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