This paper discusses a class of fractional Langevin equations on a star graph with mixed boundary conditions. Using Schaefer's fixed point theorem and Banach contraction mapping principle, the existence and uniqueness of solutions are established. Finally, two examples are constructed to illustrate the application of the obtained results. This study provides new results that enrich the existing literature on the fractional boundary value problem for graphs.
Keywords: boundary value problem; existence and uniqueness; fixed point theorem; fractional Langevin equation; star graph.