Baleanu, DumitruPaul, Supriya KumarMishra, Lakshmi NarayanMishra, Vishnu NarayanBaleanu, Dumitru2024-05-272024-05-272023Paul, Supriya Kumar...et al. (2023). "An e ffective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator", AIMS Mathematics, Vol. 8, No. 8, pp. 17448-17469.2473-6988https://hdl.handle.net/20.500.12416/8410In this paper, under some conditions in the Banach space C([0; beta];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];R). Also, we propose an e ffective and e fficient 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.eninfo:eu-repo/semantics/openAccessRiemann-Liouville Fractional IntegralFixed Point TheoremLaguerre PolynomialsHyers-Ulam StabilityHyers-Ulam-Rassias StabilityArticle88174481746910.3934/math.2023891