SOLVABILITY OF LANGEVIN FRACTIONAL DIFFERENTIAL EQUATION OF HIGHER-ORDER WITH INTEGRAL BOUNDARY CONDITIONS

This paper we concern the solvability and uniqueness of higher-order Langevin fractional differential equations subject to integral boundary conditions. We establish the existence of solutions using Krasnoselskii's fixed point theorem, while uniqueness is demonstrated through the application of the Banach fixed point theorem. The obtained results offer insights into the solution space of these complex differential equations, shedding light on their behavior and properties. To illustrate the practical implications of our findings, we provide a concrete example at the end of this paper.