In this paper we establish Hyers-Ulam-Rassias stability of a generalized functional equation in fuzzy Banach spaces. The concept originated from Th. M. Rassias theorem that appeared his paper: On the linear mapping spaces, Proc. Amer. Math. Soc. 72 (1978), 297-30.

In this study, we examine the existence and Hyers–Ulam stability of a coupled system generalized Liouville–Caputo fractional order differential equations with integral boundary conditions connection to Katugampola integrals. first third theorems, Leray–Schauder alternative Krasnoselskii’s fixed point theorem are used demonstrate solution. The Banach theorem’s concept contraction mapping is in s...

Keywords---Hyers-Ulam-Rassias stability, Functional equation, Riemann zeta function, Square root spital. 1. I N T R O D U C T I O N The staxting point of studying the stability of functional equations seems to be the famous talk of Ulam [2] in 1940, in which he discussed a number of important unsolved problems. Among those was the question concerning the stability of group homomorphisms. Let G1...

and Applied Analysis 3 where the function f z is analytic in simply connected region of the complex z-plane C containing the origin, and the multiplicity of z − ζ −α is removed by requiring log z − ζ to be real when z − ζ > 0. Definition 2.2. The fractional integral of order α > 0 is defined, for a function f z , by