January 1, 2025Open Access

Impulsive Fractional Boundary Value Problems Involving Volterra–Fredholm Integral Operators

Key Points

Existence and uniqueness results are established for impulsive fractional boundary value problems involving integral operators.
The proposed hybrid fixed-point method combines the Banach contraction principle with Krasnoselskii’s theorem, showcasing analytical advancements.
An example illustrates the applicability of the proposed approach to nonlinear integrodifferential equations.
This research provides novel insights into handling nonlocal effects in systems subjected to impulsive changes.

Abstract

This article investigates a class of nonlinear impulsive fractional integrodifferential equations involving Riemann–Liouville fractional derivatives and integral boundary conditions. The model incorporates Volterra– Fredholm integral operators to represent both memory effects and nonlocal interactions in systems experiencing impulsive changes. To address the analytical challenges posed by the nonlocal and impulsive features, we develop a novel hybrid fixed-point approach that combines the Banach contraction principle with Krasnoselskii’s theorem in Banach spaces. We establish rigorous existence and uniqueness results under suitable conditions. A detailed example is provided to demonstrate the effectiveness and applicability of the proposed method.OPEN ACCESS Received: 02/05/2025 Accepted: 27/06/2025 Published: 15/08/2025

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