On a generalized Caputo for Langevin fractional differential equations in Banach spaces

In this research article, we study the existence, uniqueness and Ulam-Hyers stability of solutions in connection to the generalized Caputo Langevin fractional differential equations in Banach Space. The existence, uniqueness, and stability in the sense of Ulam are established for the proposed system. Our approach is based on the technique of measure of noncompactness combined with the Monch fixed point theorem, the implementation Banach contraction principle fixed point theorem.  Moreover,  the Ulam--Hyers stability is discussed by utilizing the Urs's. Lastly, we deliver an example to check the efficiency and accuracy of the proposed methods.