relation: https://khub.utp.edu.my/scholars/14221/
title: Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel
creator: Kamal, R.
creator: Kamran
creator: Rahmat, G.
creator: Ahmadian, A.
creator: Arshad, N.I.
creator: Salahshour, S.
description: In this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo�Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently. © 2021, The Author(s).
publisher: Springer Science and Business Media Deutschland GmbH
date: 2021
type: Article
type: PeerReviewed
identifier:   Kamal, R. and Kamran and Rahmat, G. and Ahmadian, A. and Arshad, N.I. and Salahshour, S.  (2021) Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel.  Advances in Difference Equations, 2021 (1).   ISSN 16871839     
relation: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85109124624&doi=10.1186%2fs13662-021-03472-z&partnerID=40&md5=1d298298fb9f0a68e3d39f16792af722
relation: 10.1186/s13662-021-03472-z
identifier: 10.1186/s13662-021-03472-z