Hyers–Ulam–Rassias Stabilities of Some Classes of Fractional Differential Equations

Some years ago, the Hyers-Ulam and Hyers-Ulam-Rassias stabilities have been studied and analyzed in the case of fractional integro-differential equations. This chapter provides definitions and preliminary results on the generalized Riemann-Liouville fractional integro-differentiation operators and the Caputo fractional derivative. It introduces the stabilities of Hyers-Ulam and Hyler-Ulam-Rassias type for the considered fractional integro-differential equations. The chapter presents sufficient conditions for the Hyers-Ulam-Rassias and Hylers-Ulam stabilities, respectively, of the considered fractional integro-differential equations in a finite interval. It is devoted to study the Hyers-Ulam-Rassias stabilities of the fractional integro-differential equations in an infinite interval. The chapter presents the sufficient conditions for the Hyers-Ulam-Rassias stability of the fractional integro-differential Equations. The study of the Hyers-Ulam stability and the Hyler-Ulam-Rassias stability of some good-enough classes of integro-differentiation fractional equations leads to generalize and extend some classical results.