Stability analysis of solutions and existence theory of fractional Lagevin equation

Abstract The present article describes fractional Langevin equations (FDEs) invloving Caputo Hadamard-derivative of independent orders connected with non-local integral and non-periodic boundary conditions. The stability, existence, and uniqueness (EU) of solutions for the prescribed equations are defined. Our viewpoint is built on the specification of the Krasnoselskii fixed point theorem and the Banach contraction mapping principle. An application is offered to smooth the comprehension of the hypothetical outcomes.