Haar Wavelet Method for Numerical Solution of Two-Dimensional Partial Fractional Integro-Differential Equations

Subject Areas : International Journal of Mathematical Modelling & Computations

Ruhollah Takhtipour ¹ , Laleh Hooshangian ^{2 *} , Sara Shokrolahi Yancheshmeh ³ , Jafar Esmaily ⁴

1 - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
2 - Department of Mathematics, Dezful Branch, Islamic Azad University, Dezful, Iran.
3 - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
4 - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.

Received: 2024-06-02 Accepted : 2024-08-19 Published : 2024-09-01

Keywords: Haar wavelet method, Derivative fractional, Error analysis, Numerical solution, Two-dimensional integrodifferential equation.,

Abstract :

This article examines new methods for solving fractional integral differential equations of Fredholm using wavelets. In this research, first, fractional integral differential equations and their special properties are introduced. Then, the importance of using wavelets as a tool for analyzing and solving these equations is explained.

Wavelet methods have many advantages due to their ability to display signals and analyze nonlinear and indirect data, especially in complex and dynamic problems. The article describes various algorithms and techniques that, by utilizing the properties of wavelets, can be used to achieve numerical and analytical solutions of the above equations.

Convergence results and error evaluation are also presented in this article using examples to demonstrate the effectiveness and high efficiency of wavelet methods in solving fractional integral differential equations of Fredholm. It also reduces the variable-order fractional derivative theorem to a system of algebraic equations by approximating the Haar wavelet and integrating it.

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