Study of nonlinear boundary value hybrid fractional integro-differential equations with infinite delay

Abstract

In this study, we establish sufficient conditions for the existence of solutions to a nonlinear boundary value hybrid fractional integro-differential equation with infinite delay, incorporating the generalized fractional proportional Caputo derivative of order 1 < θ < 2. To analyze the existence of solutions for the given problem, we utilize the theory of infinite delay along with Dhage’s fixed point theorem. Finally, we present two illustrative examples to emphasize the key findings.