Browsing by Author "Paul, Supriya Kumar"

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An e ffective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator
(2023) Baleanu, Dumitru; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; 56389
In 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.
An effective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator
(2023) Baleanu, Dumitru; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; 56389
In this paper, under some conditions in the Banach space C([0, β], 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, β], 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.
Analysis of mixed type nonlinear Volterra–Fredholm integral equations involving the Erdélyi–Kober fractional operator
(2023) Baleanu, Dumitru; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; 56389
This paper investigates the existence, uniqueness and stability of solutions to the nonlinear Volterra–Fredholm integral equations (NVFIE) involving the Erdélyi–Kober (E–K) fractional integral operator. We use the Leray–Schauder alternative and Banach's fixed point theorem to examine the existence and uniqueness of solutions, and we also explore Hyers–Ulam (H–U) and Hyers–Ulam–Rassias (H–U–R) stability in the space C([0,β],R). Furthermore, three solution sets Uσ,λ, Uθ,1 and U1,1 are constructed for σ>0, λ>0, and θ∈(0,1), and then we obtain local stability of the solutions with some ideal conditions and by using Schauder fixed point theorem on these three sets, respectively. Also, to achieve the goal, we choose the parameters for the NVFIE as δ∈( [Formula presented], 1), ρ∈(0,1), γ>0. Three examples are provided to clarify the results.