Title: A pantograph-type fractional integrodifferential equation with mixed boundary conditions employing the Ψ-Caputo fractional derivative

Authors: D. Prabu

Addresses: Department of Mathematics, Sri Shakthi Institute of Engineerig and Technology, Coimbatore – 62, India

Abstract: This paper introduces a novel approach for solving pantograph-type fractional integrodifferential equations with mixed boundary conditions, utilising the Ψ-Caputo fractional derivative. This generalised operator extends traditional fractional derivatives, enabling the model to capture intricate dynamic behaviours with greater precision. The study rigorously establishes the existence and uniqueness of solutions through the Banach and Schaefer fixed point theorems, highlighting new theoretical insights into the behaviour of fractional systems under mixed boundary conditions. These findings not only expand the applicability of fractional calculus in complex real-world modelling but also contribute significant advancements to the field. An illustrative example is provided to validate the theoretical results and underscore the practical relevance of the proposed methodology.

Keywords: fractional differential equation; pantograph differential equation; fixed point theorems.

DOI: 10.1504/IJDSDE.2024.145220

International Journal of Dynamical Systems and Differential Equations, 2024 Vol.13 No.5, pp.441 - 453

Received: 03 Oct 2024
Accepted: 09 Dec 2024
Published online: 26 Mar 2025 *

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