Qualitative Analysis for Multiterm Langevin Systems with Generalized Caputo Fractional Operators of Different Orders

Abstract

In this research work, we study two types of fractional boundary value problems for multi-term Langevin systems with generalized Caputo fractional operators of different orders. The existence and uniqueness results are acquired by applying Sadovskii’s and Banach’s fixed point theorems, whereas the guarantee of the existence of solutions is shown by Ulam–Hyer’s stability. Our reported results cover many outcomes as special cases. An example is provided to illustrate and validate our results.