Boundary value problem defined by system of generalized Sturm–Liouville and Langevin Hadamard fractional differential equations.

In this paper, we study boundary value problem of system of generalized Sturm–Liouville and Langevin Hadamard fractional differential equations. Existence and uniqueness results are proved via Banach contraction principle and Leray–Schauder fixed point theorem. Besides, the Ulam–Hyers and Ulam–Hyers–Rassias stability results are addressed for the proposed problem. An example illustrating the effectiveness of the theoretical results is presented. [ABSTRACT FROM AUTHOR]