A highly accurate wavelet approach for multi-term variable-order fractional multi-dimensional differential equations

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.

Abstract

In this work, the multi-term variable-order fractional multi-dimensional differential equations are studied based on Gegenbauer wavelet functions. The main aim of this paper is to develop the spectral method with the help of modified operational matrices which are directly effective in the numerical process. Therefore, we discuss the novel method of obtaining the modified operational matrices of integration and variable-order (VO) fractional derivative. Then, the overall algorithm for solving multi-term VO-fractional differential equations and partial differential equations is introduced. We also discuss error analysis in detail. At last, we implement the numerical scheme in several examples which involve the damped mechanical oscillator equation, VO-fractional mobile-immobile advectiondispersion equation and VO-fractional nonlinear Galilei invariant advection-diffusion equation. Also, to confirm the theoretical results and demonstrate the accuracy and efficiency of the method, we compare our numerical results with analytical solutions and other existing methods.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 12 October 2024

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History

  • Receive Date: 12 August 2024
  • Revise Date: 01 October 2024
  • Accept Date: 08 October 2024

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