An effective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator
In this paper, under some conditions in the Banach space $ C ([0, \beta], \mathbb{R}) $, we establish the existence and uniqueness of the solution for the nonlinear integral equations involving the Riemann-Liouville fractional operator (RLFO). To establish the requirements for the existence and uniq...
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AIMS Press
2023-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023891?viewType=HTML |
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| author | Supriya Kumar Paul Lakshmi Narayan Mishra Vishnu Narayan Mishra Dumitru Baleanu |
| author_facet | Supriya Kumar Paul Lakshmi Narayan Mishra Vishnu Narayan Mishra Dumitru Baleanu |
| author_sort | Supriya Kumar Paul |
| collection | DOAJ |
| description | In this paper, under some conditions in the Banach space $ C ([0, \beta], \mathbb{R}) $, we establish the existence and uniqueness of the solution for the nonlinear integral equations involving the Riemann-Liouville fractional operator (RLFO). To establish the requirements for the existence and uniqueness of solutions, we apply the Leray-Schauder alternative and Banach's fixed point theorem. We analyze Hyers-Ulam-Rassias (H-U-R) and Hyers-Ulam (H-U) stability for the considered integral equations involving the RLFO in the space $ C([0, \beta], \mathbb{R}) $. Also, we propose an effective and efficient computational method based on Laguerre polynomials to get the approximate numerical solutions of integral equations involving the RLFO. Five examples are given to interpret the method. |
| first_indexed | 2024-03-13T07:12:26Z |
| format | Article |
| id | doaj.art-f535cf69a4904c729df227b7f11afa41 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T07:12:26Z |
| publishDate | 2023-05-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj.art-f535cf69a4904c729df227b7f11afa412023-06-06T01:07:07ZengAIMS PressAIMS Mathematics2473-69882023-05-0188174481746910.3934/math.2023891An effective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operatorSupriya Kumar Paul 0Lakshmi Narayan Mishra1Vishnu Narayan Mishra2Dumitru Baleanu31. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632 014, Tamil Nadu, India1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632 014, Tamil Nadu, India2. Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, 484 887, Madhya Pradesh, India3. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, 09790, Turkey 4. Institute of Space Sciences, 077125 Magurele, Ilfov, Romania 5. Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, Beirut, 11022801, LebanonIn this paper, under some conditions in the Banach space $ C ([0, \beta], \mathbb{R}) $, we establish the existence and uniqueness of the solution for the nonlinear integral equations involving the Riemann-Liouville fractional operator (RLFO). To establish the requirements for the existence and uniqueness of solutions, we apply the Leray-Schauder alternative and Banach's fixed point theorem. We analyze Hyers-Ulam-Rassias (H-U-R) and Hyers-Ulam (H-U) stability for the considered integral equations involving the RLFO in the space $ C([0, \beta], \mathbb{R}) $. Also, we propose an effective and efficient computational method based on Laguerre polynomials to get the approximate numerical solutions of integral equations involving the RLFO. Five examples are given to interpret the method.https://www.aimspress.com/article/doi/10.3934/math.2023891?viewType=HTMLriemann-liouville fractional integralfixed point theoremlaguerre polynomialshyers-ulam stabilityhyers-ulam-rassias stability |
| spellingShingle | Supriya Kumar Paul Lakshmi Narayan Mishra Vishnu Narayan Mishra Dumitru Baleanu An effective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator AIMS Mathematics riemann-liouville fractional integral fixed point theorem laguerre polynomials hyers-ulam stability hyers-ulam-rassias stability |
| title | An effective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator |
| title_full | An effective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator |
| title_fullStr | An effective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator |
| title_full_unstemmed | An effective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator |
| title_short | An effective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator |
| title_sort | effective method for solving nonlinear integral equations involving the riemann liouville fractional operator |
| topic | riemann-liouville fractional integral fixed point theorem laguerre polynomials hyers-ulam stability hyers-ulam-rassias stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023891?viewType=HTML |
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