A study of a Coupled System of Fractional Differential Equations with Two Points Integral Boundary Conditions (European Journal of Pure and Applied Mathematics, 2025)
In this paper, a certain system of fractional differential equations of integral boundary conditions BCs at two points is discussed. The presented coupled fractional system are useful for describing real-world phenomena, such as in physics, biology, and engineering. By utilizing the contraction mapping principle, we demonstrate uniqueness of certain solutions of the given system. Next, we utilize the contraction mapping principle to prove uniqueness of each solution. Further, we address the Hyers-Ulam stability and provide its conditions to show that small changes in the input lead to small changes in the result. Moreover, we provide numerical examples to support and demonstrate our theoretical results.
Keywords: Coupled system, fractional differential equation, fractional derivative, Hyers-Ulam stability, fixed point theorem.