Numerical Investigation of the Fractional Diffusion Wave Equation with the Mittag–Leffler Function-Reference-Cited by-同舟云学术

Numerical Investigation of the Fractional Diffusion Wave Equation with the Mittag–Leffler Function

Published:2023-12-26 Issue:1 Volume:8 Page:18
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Shafiq Madiha¹^ORCID,Abbas Muhammad¹^ORCID,El-Shewy Emad K.²³^ORCID,Abdelrahman Mahmoud A. E.⁴⁵^ORCID,Abdo Noura F.⁴⁵,El-Rahman Ali A.⁶⁷^ORCID

Affiliation:

1. Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

2. Department of Physics, College of Science, Taibah University, Al-Madinah Al-Munawarah 41411, Saudi Arabia

3. Theoretical Physics Group, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

4. Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 41411, Saudi Arabia

5. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

6. Department of Physics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

7. Department of Physics, Faculty of Science, The New Valley University, Kharga Oasis 72714, Egypt

Abstract

A spline is a sufficiently smooth piecewise curve. B-spline functions are powerful tools for obtaining computational outcomes. They have also been utilized in computer graphics and computer-aided design due to their flexibility, smoothness and accuracy. In this paper, a numerical procedure dependent on the cubic B-spline (CuBS) for the time fractional diffusion wave equation (TFDWE) is proposed. The standard finite difference (FD) approach is utilized to discretize the Atangana–Baleanu fractional derivative (ABFD), while the derivatives in space are approximated through the CuBS with a θ-weighted technique. The stability of the propounded algorithm is analyzed and proved to be unconditionally stable. The convergence analysis is also studied, and it is of the order O(h2+(Δt)2). Numerical solutions attained by the CuBS scheme support the theoretical solutions. The B-spline technique gives us better results as compared to other numerical techniques.

Funder

Deputyship for Research & Innovation of the Ministry of Education of Saudi Arabia

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/8/1/18/pdf

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