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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| Published in | AIMS mathematics Vol. 8; no. 8; pp. 17448 - 17469 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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AIMS Press
2023
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2473-6988 2473-6988 |
| DOI | 10.3934/math.2023891 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Baleanu, Dumitru Mishra, Vishnu Narayan Paul, Supriya Kumar Mishra, Lakshmi Narayan |
| Author_xml | – sequence: 1 givenname: Supriya Kumar surname: Paul fullname: Paul, Supriya Kumar organization: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632 014, Tamil Nadu, India – sequence: 2 givenname: Lakshmi Narayan surname: Mishra fullname: Mishra, Lakshmi Narayan organization: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632 014, Tamil Nadu, India – sequence: 3 givenname: Vishnu Narayan surname: Mishra fullname: Mishra, Vishnu Narayan organization: Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, 484 887, Madhya Pradesh, India – sequence: 4 givenname: Dumitru surname: Baleanu fullname: Baleanu, Dumitru organization: Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, 09790, Turkey, Institute of Space Sciences, 077125 Magurele, Ilfov, Romania, Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, Beirut, 11022801, Lebanon |
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| Title | An effective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator |
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