Laplace transform method for a coupled system of (p, q)-Caputo fractional differential equations

This research uses the Laplace transform method to analyze a coupled system of (p, q)-Caputo fractional differential equations, employing the (p, q)-generalized Caputo derivative. This system includes a function with a Volterra integral operator and integral kernel. By applying the Laplace transform method, we transform the differential equations into algebraic equations in the Laplace domain, which facilitates a systematic analysis of the system’s dynamics and stability properties. Furthermore, we examine the existence and uniqueness of solutions with initial conditions using Shaefer’s fixed point theorem and the Banach fixed point theorem in Banach space. Additionally, we explore the stability of the relevant solutions of the Ulam–Hyers (UH) type. An illustrative example will be presented to demonstrate the theoretical findings.