EXISTENCE AND STABILITY RESULTS OF FRACTIONAL DIFFERENTIAL EQUATIONS MITTAG-LEFFLER KERNEL

Abstract

This paper presents the following AB-Caputo fractional boundary value problem (ABC)(0)D(alpha)u(sigma) = G(sigma, u(sigma)), sigma is an element of[0, 1] with integral-type boundary conditions u(0) = 0 = u ''(0), gamma u(1) = lambda integral(1)(0) g(1)(kappa)u(kappa)d kappa, of order 2 < alpha <= 3. Schauder and Krasnoselskii's fixed point theorems are used to find existence results. Uniqueness is obtained via the Banach contraction principle. To investigate the stability of a given problem, Hyers-Ulam stability is discussed. An example is provided to validate our results.