Analytical and numerical techniques for solving a fractional integro-differential equation in complex space

Amnah E. Shammaky; Eslam M. Youssef; Amnah E. Shammaky; Eslam M. Youssef

doi:10.3934/math.20241543

AIMS Mathematics

2024, Volume 9, Issue 11: 32138-32156. doi: 10.3934/math.20241543

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Analytical and numerical techniques for solving a fractional integro-differential equation in complex space

Amnah E. Shammaky ¹,
Eslam M. Youssef ^{2
,
,}

1.
Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
2.
Department of Mathematics, Faculty of Education, Alexandria University, Alexandria 21256, Egypt

Received: 26 July 2024 Revised: 29 October 2024 Accepted: 01 November 2024 Published: 13 November 2024
MSC : 26A33, 34A34, 34D05, 34K20, 65L05

In this article, we describe the existence and uniqueness of a solution to the nonlinear fractional Volterra integro differential equation in complex space using the fixed-point theory. We also examine the remarkably effective Euler wavelet method, which converts the model to a matrix structure that lines up with a system of algebraic linear equations; this method then provides approximate solutions for the given problem. The proposed technique demonstrates superior accuracy in numerical solutions when compared to the Euler wavelet method. Although we provide two cases of computational methods using MATLAB R2022b, which could be the final step in confirming the theoretical investigation.
- fractional calculus,
- complex plane,
- fixed point theorem,
- rationalized Haar wavelet,
- Euler wavelet method
Citation: Amnah E. Shammaky, Eslam M. Youssef. Analytical and numerical techniques for solving a fractional integro-differential equation in complex space[J]. AIMS Mathematics, 2024, 9(11): 32138-32156. doi: 10.3934/math.20241543

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Abstract

In this article, we describe the existence and uniqueness of a solution to the nonlinear fractional Volterra integro differential equation in complex space using the fixed-point theory. We also examine the remarkably effective Euler wavelet method, which converts the model to a matrix structure that lines up with a system of algebraic linear equations; this method then provides approximate solutions for the given problem. The proposed technique demonstrates superior accuracy in numerical solutions when compared to the Euler wavelet method. Although we provide two cases of computational methods using MATLAB R2022b, which could be the final step in confirming the theoretical investigation.

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