Conformable finite element method for conformable fractional partial differential equations

Lakhlifa Sadek; Tania A Lazǎr; Ishak Hashim; Lakhlifa Sadek; Tania A Lazǎr; Ishak Hashim

doi:10.3934/math.20231479

AIMS Mathematics

2023, Volume 8, Issue 12: 28858-28877. doi: 10.3934/math.20231479

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Conformable finite element method for conformable fractional partial differential equations

1.
Faculty of Sciences and Technology, BP 34. Ajdir 32003 Al-Hoceima, Abdelmalek Essaadi University, Tétouan, Morocco
2.
Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj Napoca, Romania
3.
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), Bangi 43650, Selangor, Malaysia
4.
Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates

Received: 13 August 2023 Revised: 29 September 2023 Accepted: 16 October 2023 Published: 24 October 2023
MSC : 26A33, 34A12

The finite element (FE) method is a widely used numerical technique for approximating solutions to various problems in different fields such as thermal diffusion, mechanics of continuous media, electromagnetism and multi-physics problems. Recently, there has been growing interest among researchers in the application of fractional derivatives. In this paper, we present a generalization of the FE method known as the conformable finite element method, which is specifically designed to solve conformable fractional partial differential equations (CF-PDE). We introduce the basis functions that are used to approximate the solution of CF-PDE and provide error estimation techniques. Furthermore, we provide an illustrative example to demonstrate the effectiveness of the proposed method. This work serves as a starting point for tackling more complex problems involving fractional derivatives.
- CCF-PDE,
- Galerkin method,
- conformable finite element (CFE) method
Citation: Lakhlifa Sadek, Tania A Lazǎr, Ishak Hashim. Conformable finite element method for conformable fractional partial differential equations[J]. AIMS Mathematics, 2023, 8(12): 28858-28877. doi: 10.3934/math.20231479

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Abstract

The finite element (FE) method is a widely used numerical technique for approximating solutions to various problems in different fields such as thermal diffusion, mechanics of continuous media, electromagnetism and multi-physics problems. Recently, there has been growing interest among researchers in the application of fractional derivatives. In this paper, we present a generalization of the FE method known as the conformable finite element method, which is specifically designed to solve conformable fractional partial differential equations (CF-PDE). We introduce the basis functions that are used to approximate the solution of CF-PDE and provide error estimation techniques. Furthermore, we provide an illustrative example to demonstrate the effectiveness of the proposed method. This work serves as a starting point for tackling more complex problems involving fractional derivatives.

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