Existence, Uniqueness, and Stability of a Nonlinear Tripled Fractional Order Differential System

Abstract

This manuscript investigates the existence, uniqueness, and different forms of Ulam stability for a system of three coupled differential equations involving the Riemann–Liouville (RL) fractional operator. The Leray–Schauder alternative is employed to confirm the existence of solutions, while the Banach contraction principle is used to establish their uniqueness. Stability conditions are derived utilizing classical nonlinear functional analysis techniques. Theoretical findings are illustrated with an example. The proposed system generalizes third-order ordinary differential equations (ODEs) with different boundary conditions (BCs).

Keywords

• fractional derivatives
• differential equations
• nonlinear equations
• nonlinear systems
• existence theory
• Ulam stability