Existence theory and Ulam’s stabilities for switched coupled system of implicit impulsive fractional order Langevin equations

Abstract

Abstract In this work, a system of nonlinear, switched, coupled, implicit, impulsive Langevin equations with two Hilfer fractional derivatives is introduced. The suitable conditions and results are established to discuss existence, uniqueness, and Ulam-type stability results of the mentioned model, with the help of nonlinear functional analysis techniques and Banach’s fixed-point theorem. Furthermore, we examine our results with the help of example.

Keywords

• Langevin equation
• Hilfer fractional derivative
• Ulam–Hyers–Rassias stability