10.1007/s40096-023-00510-7

Space-time pseudospectral method for the variable-order space-time fractional diffusion equation

  • Rupali Gupta*1,
  • Sushil Kumar1,
  1. Department of Mathematics and Humanities, S. V. National Institute of Technology Surat, Surat, Gujarat, 395007, IN

Published in Issue 2023-02-21

How to Cite

Gupta, R., & Kumar, S. (2023). Space-time pseudospectral method for the variable-order space-time fractional diffusion equation. Mathematical Sciences, 18(3 (September 2024). https://doi.org/10.1007/s40096-023-00510-7
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Abstract

Abstract In this paper, we study the space-time variable-order fractional diffusion equation with a variable diffusion coefficient. The fractional derivatives of variable orders are considered in the Caputo sense. We propose a numerically efficient pseudospectral method with the Chebyshev polynomials as orthogonal basis functions. Also, we examine the error bound and convergence analysis of the approximate solution. A variation in the maximum absolute error with the different variable orders in space and time is studied. Some illustrative examples are presented with different boundary conditions, e.g., Dirichlet, mixed, and non-local. The method’s applicability is also tested with the problem of owning fractional power in the solution. The results obtained from the proposed approach demonstrate the efficacy and reliability of the method.

Keywords

  • Variable-order space-time fractional diffusion equation,
  • Caputo’s variable-order fractional derivative,
  • Pseudospectral method,
  • Chebyshev polynomials

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