Existence and uniqueness of solutions to a certain Caputo fractional delay integral boundary value problem

This work investigated the existence and uniqueness of solutions to a certain Caputo fractional delay integral boundary value problem. Using Sadovskii’s fixed point theorem, we establish the existence and uniqueness of solutions to this problem. As a specific example, we consider a non-homogeneous two-term problem with deviating argument under integral boundary conditions. We obtained explicit solutions using the Laplace transform method, and analyzed the phase portraits of the system for all values of α ∈ (0, 1) and the two-parameter Mittag–Leffler function to establish the viability of our solution in real-life applications.