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...
| Main Authors: | , , , , , , |
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| Format: | Article |
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World Scientific Publishing
2021
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| Online Access: | http://psasir.upm.edu.my/id/eprint/100104/ |
| _version_ | 1848863225055019008 |
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| author | Amin, Rohul Senu, Norazak Hafeez, Muhammad Bilal Arshad, Noreen Izza Ahmadian, Ali Salahshour, Soheil Sumelka, Wojciech |
| author_facet | Amin, Rohul Senu, Norazak Hafeez, Muhammad Bilal Arshad, Noreen Izza Ahmadian, Ali Salahshour, Soheil Sumelka, Wojciech |
| author_sort | Amin, Rohul |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T13:29:32Z |
| format | Article |
| id | upm-100104 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:29:32Z |
| publishDate | 2021 |
| publisher | World Scientific Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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 |
| 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 |
| title | 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_short | 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 |
| url | http://psasir.upm.edu.my/id/eprint/100104/ http://psasir.upm.edu.my/id/eprint/100104/ http://psasir.upm.edu.my/id/eprint/100104/ |