On the new fractional configurations of integro-differential Langevin boundary value problems

In this paper, we present the existence criteria for the solutions of boundary value problems involving generalized fractional integro-Langevin equation and inclusion supplemented with nonlocal fractional boundary conditions. The main idea of the current research is to combine the integro-differential and Langevin structures together. The main tools of our study include certain inequalities and well-known fixed point theorems. Numerical examples are constructed to demonstrate the application of the obtained results.