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

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...

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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
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spelling my.upm.eprints.1001042024-08-01T04:02:23Z http://psasir.upm.edu.my/id/eprint/100104/ A computational algorithm for the numerical solution of nonlinear fractional integral equations Amin, Rohul Senu, Norazak Hafeez, Muhammad Bilal Arshad, Noreen Izza Ahmadian, Ali Salahshour, Soheil Sumelka, Wojciech 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. World Scientific Publishing 2021-12-28 Article PeerReviewed Amin, Rohul and Senu, Norazak and Hafeez, Muhammad Bilal and Arshad, Noreen Izza and Ahmadian, Ali and Salahshour, Soheil and Sumelka, Wojciech (2021) A computational algorithm for the numerical solution of nonlinear fractional integral equations. Fractals, 30 (1). art. no. 2240030. pp. 1-8. ISSN 0218-348X; ESSN: 1793-6543 https://www.worldscientific.com/doi/abs/10.1142/S0218348X22400308 10.1142/S0218348X22400308
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
description 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.
format Article
author Amin, Rohul
Senu, Norazak
Hafeez, Muhammad Bilal
Arshad, Noreen Izza
Ahmadian, Ali
Salahshour, Soheil
Sumelka, Wojciech
spellingShingle Amin, Rohul
Senu, Norazak
Hafeez, Muhammad Bilal
Arshad, Noreen Izza
Ahmadian, Ali
Salahshour, Soheil
Sumelka, Wojciech
A computational algorithm for the numerical solution of nonlinear fractional integral equations
author_facet Amin, Rohul
Senu, Norazak
Hafeez, Muhammad Bilal
Arshad, Noreen Izza
Ahmadian, Ali
Salahshour, Soheil
Sumelka, Wojciech
author_sort Amin, Rohul
title A computational algorithm for the numerical solution of nonlinear fractional integral equations
title_short A computational algorithm for the numerical solution of nonlinear fractional integral equations
title_full A computational algorithm for the numerical solution of nonlinear fractional integral equations
title_fullStr A computational algorithm for the numerical solution of nonlinear fractional integral equations
title_full_unstemmed A computational algorithm for the numerical solution of nonlinear fractional integral equations
title_sort computational algorithm for the numerical solution of nonlinear fractional integral equations
publisher World Scientific Publishing
publishDate 2021
url http://psasir.upm.edu.my/id/eprint/100104/
https://www.worldscientific.com/doi/abs/10.1142/S0218348X22400308
_version_ 1806446351781724160
score 13.211869

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