Darweesh Amer, Al-Khaled Kamel, Al-Yaqeen Omar Abu
Department of Mathematics and Statistics, Jordan University of Science & Technology, Irbid, Jordan.
Heliyon. 2023 Sep 9;9(9):e19717. doi: 10.1016/j.heliyon.2023.e19717. eCollection 2023 Sep.
In this paper, firstly, the " Haar wavelet method " is used to give approximate solutions for coupled systems of linear fractional Fredholm integro-differential equations. Moreover, we consider the fractional derivative to be described in the Caputo sense. The general idea of this technique is simply based on reducing this kinds of coupled systems into systems of algebraic equations which are easily to deal with and solve. Also, Laplace transform operator is included to develop a sophisticated approach which we called " Laplace Haar wavelet method " as an adjustment to " Haar wavelet method " to reduce the error and computational time. We provide illustrative examples to confirm validity, efficiency, accuracy, and applicability of the proposed methods.
在本文中，首先，使用“哈尔小波方法”给出线性分数阶弗雷德霍姆积分 - 微分方程耦合系统的近似解。此外，我们考虑分数阶导数是在卡普托意义下描述的。该技术的总体思路仅仅是基于将这类耦合系统简化为易于处理和求解的代数方程组。同时，引入拉普拉斯变换算子来开发一种复杂的方法，我们称之为“拉普拉斯哈尔小波方法”，作为对“哈尔小波方法”的一种调整，以减少误差和计算时间。我们提供了示例来说明所提出方法的有效性、效率、准确性和适用性。
