On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders

In this paper we develop the existence theory for a nonlinear Langevin equation involving Caputo fractional derivatives of different orders and Riemann–Liouville fractional integral supplemented with nonlocal multi-point and multi-strip boundary conditions. We make use of the modern methods of functional analysis to obtain the existence and uniqueness results for the given problem, which are well illustrated with the aid of examples. Our results are new and correspond to some new ones for specific choices of the parameters involved in the problem.