A computational algorithm for the numerical solution of nonlinear fractional integral equations

• Main Authors: Amin, Rohul, Senu, Norazak, Hafeez, Muhammad Bilal, Arshad, Noreen Izza, Ahmadian, Ali, Salahshour, Soheil, Sumelka, Wojciech
• Format: Article
• Published: World Scientific Publishing 2021
• Online Access: http://psasir.upm.edu.my/id/eprint/100104/; https://www.worldscientific.com/doi/abs/10.1142/S0218348X22400308
• Institution: Universiti Putra Malaysia

In this paper, we develop a numerical method for the solution of nonlinear fractional integralequations (NFIEs) based on Haar wavelet collocation technique (HWCT). Under certain con-ditions, we also prove the uniqueness and existence as well as Hyers–Ulam (HU) stability of thesolution. With the help of the mentioned technique, the considered problem is transformed toa system of algebraic equations which is then solved for the required results by using Broydenalgorithm. To check the validation and convergence of the proposed technique, some exam-ples are given. For different number of collocation points (CPs), maximum absolute and meansquare root errors are computed. The results show that for solving these equations, the HWCTis effective. The convergence rate is also measured for different CPs, which is nearly equal to 2.