Browsing by Author "Halder, Sukanta"

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A Study on the Solvability of Fractional Integral Equation in a Banach Algebra Via Petryshyn's Fixed Point Theorem
(Taylor & Francis Ltd, 2024) Halder, Sukanta; Deepmala, Cemil; Tunc, Cemil
This study focuses on the nonlinear fractional functional integral equation (FFIE) concerning the Riemann-Liouville operator. In certain weaker conditions, the authors demonstrate that the FFIE has a solution, which is defined within the Banach algebra $ C [0, a], a>0. Our analysis relies on the Petryshyn's fixed point theorem and the notion of measure of non-compactness (MNC). In addition, our results include numerous authors' work under less restrictive conditions. Furthermore, we provide an illustrative example of fractional functional integral equations to support our proven results.
An Existence Results of a Product Type Fractional Functional Integral Equations Using Petryshyn's Fixed Point Theorem
(Taylor & Francis Ltd, 2025) Halder, Sukanta; Tunc, Cemil
In this paper, we investigate the existence of solutions for a new class of nonlinear product-type fractional functional integral equations (FFIEs) involving the Riemann-Liouville fractional integral operator. To establish the existence of at least one solution, we employ Petryshyn's fixed-point theorem (PFPT) combined with the concept of the measure of noncompactness (MNC) in the Banach space $ C[0,a] $ C[0,a] of continuous functions. Unlike other approaches based on Darbo's or Schauder's fixed-point theorems in Banach algebras, our method does not require the operator to map a closed convex subset onto itself, nor does it rely on the commonly assumed "sublinear condition" for the functional involved in the equation. Therefore, our results generalize and unify several existing results in the literature under fewer conditions. Additionally, to support our theoretical findings, we provide an example of such nonlinear FFIEs, thereby illustrating the applicability of the proposed results.