On solution of fractional partial differential equation by the weighted fractional operator

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Bayrak M. A., Demir A., Ozbilge E.

Alexandria Engineering Journal, vol.59, pp.4805-4819, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59
  • Publication Date: 2020
  • Doi Number: 10.1016/j.aej.2020.08.044
  • Journal Name: Alexandria Engineering Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, Directory of Open Access Journals
  • Page Numbers: pp.4805-4819
  • Keywords: Homotopy analysis method, Residual power series method, Weighted Atangana-Baleanu fractional derivative, Weighted Caputo-Fabrizio fractional derivative, Fractional partial differential equations, SYSTEMS, MODEL, SOLITONS, DIFFUSION
  • Kocaeli University Affiliated: Yes

Abstract

 Alexandria UniversityThe motivation of this paper is to construct the solution of fractional partial differential equations (FPDEs) by the combination of Laplace transform homotopy analysis method (LHAM) and the Laplace transform residual power series method (LRPSM) with weighted Atangana-Baleanu and weighted Caputo-Fabrizio fractional derivatives with specific weighted functions. Moreover, the solutions are analyzed by comparing with exact solutions of these equations. The obtained consequences illustrate that methods LHAM and LRPSM work very well to determine the solutions of FPDEs with weighted fractional derivatives in consideration.