New fractional results for Langevin equations through extensive fractional operators

Fractional Langevin equations play an important role in describing a wide range of physical processes. For instance, they have been used to describe single-file predominance and the behavior of unshackled particles propelled by internal sounds. This article investigates fractional Langevin equations incorporating recent extensive fractional operators of different orders. Nonperiodic and nonlocal integral boundary conditions are assumed for the model. The Hyres-Ulam stability, existence, and uniqueness of the solution are defined and analyzed for the suggested equations. Also, we utilize Banach contraction principle and Krasnoselskii fixed point theorem to accomplish our results. Moreover, it will be apparent that the findings of this study include various previously obtained results as exceptional cases.