Abstract
The aim of this paper is to establish the Ulam stability of the Caputo-Fabrizio fractional differential equation with integral boundary condition. We also present the existence and uniqueness results of the solution for the Caputo-Fabrizio fractional differential equation by Krasnoselskii’s fixed point theorem and Banach fixed point theorem. Some examples are provided to illustrate our theorems.
Highlights
Ulam [1] proposed to study the approximation degree of the approximate solution and the exact solution of the equation in 1940
Researchers initiated a research on the Ulam stability of integer-order differential equations
The study on the Ulam stability of fractional differential equations is in its infancy
Summary
Ulam [1] proposed to study the approximation degree of the approximate solution and the exact solution of the equation in 1940. Hyers [2] responded to Ulam’s proposal and defined the Hyers-Ulam stability of equation in 1941. Researchers initiated a research on the Ulam stability of integer-order differential equations (see [4,5,6,7,8,9,10]). Wang et al [6] studied the Ulam stability of the first-order differential equation with a boundary value condition. Otrocol and Ilea [7] obtained the Ulam stability of the first-order delay differential equation. Huang and Li [8] obtained the Hyers-Ulam stability of another class of the first-order delay differential equation. Zada et al [9] studied the Hyers-Ulam-Rassias stability of the higher order delay differential equation. The study on the Ulam stability of fractional differential equations is in its infancy
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