A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation

Khasteh, Mohsen; Refahi Sheikhani, Amir Hosein; Shariffar, Farhad

doi:10.22034/cmde.2024.57844.2426

A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation

Document Type : Research Paper

Authors

¹ Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.

² Department of Applied Mathematics, Fouman and Shaft Branch, Islamic Azad University, Fouman, Iran.

10.22034/cmde.2024.57844.2426

Abstract

In this paper we proposed a numerical method based on the shifted fractional order
Jacobi and trapezoid methods to solve a type of distributed partial differential
equations. The fractional derivatives are considered in the Caputo-Prabhakar type.
By shifted fractional-order Jacobi polynomials our proposed method can provide
highly accurate approximate solutions by reducing the problem under study to a
set of algebraic equations which is technically simpler for handling. In order to
demonstrate the error estimates, several lemmas are provided. Finally, numerical
results are provided to demonstrate the validity of the theoretical analysis.

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Main Subjects