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Browsing by Author "Mishra, Vishnu Narayan"

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    An e ffective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator
    (2023) Paul, Supriya Kumar; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    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.
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    Article
    Citation - WoS: 23
    Citation - Scopus: 27
    Analysis of Mixed Type Nonlinear Volterra-Fredholm Integral Equations Involving the Erdelyi-Kober Fractional Operator
    (Elsevier, 2023) Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; Paul, Supriya Kumar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    This paper investigates the existence, uniqueness and stability of solutions to the nonlinear Volterra-Fredholm integral equations (NVFIE) involving the Erdelyi-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, fl], R). Furthermore, three solution sets U-sigma,U-lambda, U-theta,U-1 and U-1,U-1 are constructed for sigma > 0, lambda > 0, and theta is an element of (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 delta is an element of (1/2, 1), p is an element of (0,1), gamma > 0. Three examples are provided to clarify the results.
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    Article
    Citation - WoS: 27
    Citation - Scopus: 29
    An E Ffective Method for Solving Nonlinear Integral Equations Involving the Riemann-Liouville Fractional Operator
    (Amer inst Mathematical Sciences-aims, 2023) Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; Paul, Supriya Kumar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    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.
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    Article
    Citation - WoS: 16
    Citation - Scopus: 19
    On the Solvability of Mixed-Type Fractional-Order Non-Linear Functional Integral Equations in the Banach Space C(I)
    (Mdpi, 2022) Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; Pathak, Vijai Kumar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    This paper is concerned with the existence of the solution to mixed-type non-linear fractional functional integral equations involving generalized proportional (kappa,phi)-Riemann-Liouville along with Erdelyi-Kober fractional operators on a Banach space C([1,T]) arising in biological population dynamics. The key findings of the article are based on theoretical concepts pertaining to the fractional calculus and the Hausdorff measure of non-compactness (MNC). To obtain this goal, we employ Darbo's fixed-point theorem (DFPT) in the Banach space. In addition, we provide two numerical examples to demonstrate the applicability of our findings to the theory of fractional integral equations.