Browsing by Author "Deepmala, Cemil"

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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.