Existence and Ulam’s Stability for Conformable Fractional Differential Equations with Constant Coefficients

Abstract

In this article, we develop a standard idea in seeking the solution of linear ODEs to derive the representation of solutions to conformable fractional linear differential equations with constant coefficients by adopting the variation of constants method. In addition, we present the existence of solutions to conformable fractional nonlinear differential equations with constant coefficients under mild conditions on the nonlinear term. Also, we transfer the concepts of Ulam’s stability for ODEs to this type of equation and give the Ulam–Hyers and Ulam–Hyers–Rassias stability results on finite time and infinite time intervals.