10.1007/s40096-021-00425-1

Modified wavelet method for solving multitype variable-order fractional partial differential equations generated from the modeling of phenomena

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  • Haniye Dehestani1,
  • Yadollah Ordokhani*1,
  • Mohsen Razzaghi2,
  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IR
  2. Department of Mathematics and Statistics, Mississippi State University, Starkville, MS, 39762, US

Published in Issue 2021-07-25

How to Cite

Dehestani, H., Ordokhani, Y., & Razzaghi, M. (2021). Modified wavelet method for solving multitype variable-order fractional partial differential equations generated from the modeling of phenomena. Mathematical Sciences, 16(4 (December 2022). https://doi.org/10.1007/s40096-021-00425-1
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Abstract

Abstract The aim of this paper is to introduce a new wavelet method for presenting approximate solutions of multitype variable-order (VO) fractional partial differential equations arising from the modeling of phenomena. In specific, this paper focuses on the numerical solution of the VO-fractional mobile-immobile advection-dispersion equation, Klein Gordon equation and Burgers equation. These equations are converted into a system of algebraic equations with the assistance of the bivariate Genocchi wavelet functions, their operational matrices, and the variable-order fractional Caputo derivative operator. Also, we present a new technique to get the operational matrix of integration and VO-fractional derivative. The modified operational matrices for solving the proposed equations are powerful and effective. So that, the accuracy of these matrices directly affects the implementation process. Finally, we consider numerical examples to confirm the superiority of the scheme, and for each example, exhibit the results through graphs and tables.

Keywords

  • Genocchi wavelet functions,
  • Variable-order Caputo fractional derivative,
  • Modified operational matrix,
  • Error estimation

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