Mittag-Leffler Functions in the Integral Representation of a Class of FDEs: Existence, Stability and Numirical Study.

Abstract This paper proposes a new fractional order differential problem of Langevin type. Using Mitttag Leffler functions in the integral representation of the problem, the Banach fixed point theorem is applied to prove an existence and uniqueness result of solution for the proposed problem. Then, the existence of at least one solution is established and some illustrative examples are discussed. The stability in the sense of Ulam Hyers is also investigated. Finally, numerical simulations of the solutions are performed using Runge Kutta method in combination with decoupling and quasi-linearization techniques. Mathematics Subject Classification (2010): 26A33, 34A60, 65L06.