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Khasteh, Mohsen, Refahi Sheikhani, Amir Hosein, Shariffar, Farhad. (1403). A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation. سامانه مدیریت نشریات علمی, 12(3), 571-584. doi: 10.22034/cmde.2024.57844.2426
Mohsen Khasteh; Amir Hosein Refahi Sheikhani; Farhad Shariffar. "A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation". سامانه مدیریت نشریات علمی, 12, 3, 1403, 571-584. doi: 10.22034/cmde.2024.57844.2426
Khasteh, Mohsen, Refahi Sheikhani, Amir Hosein, Shariffar, Farhad. (1403). 'A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation', سامانه مدیریت نشریات علمی, 12(3), pp. 571-584. doi: 10.22034/cmde.2024.57844.2426
Khasteh, Mohsen, Refahi Sheikhani, Amir Hosein, Shariffar, Farhad. A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation. سامانه مدیریت نشریات علمی, 1403; 12(3): 571-584. doi: 10.22034/cmde.2024.57844.2426

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

Computational Methods for Differential Equations
مقاله 11، دوره 12، شماره 3، مهر 2024، صفحه 571-584    اصل مقاله (1.31 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.57844.2426
نویسندگان
Mohsen Khasteh1؛ Amir Hosein Refahi Sheikhani* 1؛ Farhad Shariffar2
1Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
2Department of Applied Mathematics, Fouman and Shaft Branch, Islamic Azad University, Fouman, Iran.
چکیده
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 to handle. In order to demonstrate the error estimates, several lemmas are provided. Finally, numerical results are provided to demonstrate the validity of the theoretical analysis.
کلیدواژه‌ها
Distributed order؛ Caputo-Prabhakar fractional derivative؛ Shifted Jacobi polynomials؛ Trapezoid؛ Numerical method
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