Novel results on positive solutions for nonlinear Caputo–Hadamard fractional Volterra–Fredholm integro differential equations

In this paper, we establish the existence and uniqueness of positive solutions for fractional Volterra–Fredholm integro-differential equation. This equation incorporates Caputo–Hadamard fractional derivatives and is defined with initial conditions. Our proof methodology relies on the Schauder fixed point theorem, the Banach contraction principle, upper and lower solution concepts, and their applications. To illustrate the significance of our theoretical findings, we also present a compelling example.