Langevin equation involving two fractional orders with three-point boundary conditions

Abstract

In the current manuscript, we examine the existence and uniqueness of solution for generalized Langevin equation involving two distinct fractional orders with a three-point boundary value problem. We implement the notions of fractional calculus simultaneously with immutable point types to create the existence and uniqueness results. To explore our problem, we apply the Banach contraction principle, Krasnoselskii's fixed point theorem, nonlinear alternative Leray-Schauder theorem and Leray-Schauder degree theorem. Expository examples are rended to clarify the applicability of our main results.