New technique for controllability results of Hilfer fractional hybrid Langevin dynamical system

Abstract

Our work introduces a novel type of hybrid Langevin equations that include both Riemann and Caputo fractional order derivatives. While the measure of non-compactness has become significant to fixed point theory, we apply the measure of non-compactness approach as an essential aspect for arriving at the controllability the result. The Schauder fixed point theorem is then used in a generalized version to make use of the contemporary analytic technique. To improve the comprehensibility of our findings, which we provided a numerical example.