Some Existence and Uniqueness Results for a Class of Tripled Systems of Fractional Langevin Differential Equations with Cyclic Boundary Conditions

In this study, we investigate the solvability of a tripled system of fractional Langevin differential equations subject to cyclic anti-periodic boundary conditions. We do this through the systematic derivation of explicit solution formulas involving Mittag-Leffler functions. Using fixed-point methods alongside the key properties of Mittag-Leffler functions, we establish existence and uniqueness results under weaker sufficient conditions than those used in previous studies, thereby extending the current theoretical framework. Additionally, we provide numerical examples that demonstrate the effectiveness and practical advantages of the proposed solutions.