10.1007/s40096-021-00451-z

A numerical method for nonlinear fractional reaction–advection–diffusion equation with piecewise fractional derivative

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  • M. H. Heydari*1,
  • A. Atangana2,
  1. Department of Mathematics, Shiraz University of Technology, Shiraz, IR
  2. Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, ZA Department of Medical Research China Medical University Hospital, China Medical University, Taichung, TW

Published in Issue 2022-01-12

How to Cite

Heydari, M. H., & Atangana, A. (2022). A numerical method for nonlinear fractional reaction–advection–diffusion equation with piecewise fractional derivative. Mathematical Sciences, 17(2 (June 2023). https://doi.org/10.1007/s40096-021-00451-z
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Abstract

Abstract This study introduces a new fractional version of the nonlinear reaction–advection–diffusion equation using a kind of piecewise fractional derivatives defined by Atangana and Araz. A hybrid approach using the Chebyshev cardinal functions and piecewise Chebyshev cardinal functions is established for finding a solution to this equation. The presented method transforms solving the generated fractional problem into finding the solution of a nonlinear algebraic system by expanding the solution of the problem in terms of the mentioned basis functions and employing the piecewise fractional derivative matrix of the piecewise Chebyshev cardinal functions (which is derived in this study). The accuracy of the constructed algorithm is checked in some illustrative examples.

Keywords

  • Chebyshev cardinal functions,
  • Piecewise fractional derivative,
  • Reaction–advection–diffusion equation,
  • Piecewise fractional derivative matrix

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