Ulam-Hyers stability for a nonlinear Volterra integro-differential equation

Abstract

In this work, the Ulam-Hyers stability and the Ulam-Hyers-Rassias stability for the nonlinear Volterra integro-differential equations are established by employing the method of successive approximation. Some simple examples are given to illustrate the main results.

Stability Results for a Class of Nonlinear Caputo Volterra-Fredholm System: Physics and Engineering Application

“…Because of the broad scope of fractional calculus, many authors focused on the study of stability for fractional differential equations [5][6][7][8]. In the same regard, fractional integro-differential equations also drew the attention of several authors [9][10][11][12][13][14][15][16].…”

“…The Ulam-type stability of an integro-differential equation implies that we can find the exact solution to the problem near an approximate solution. Several varieties of Ulam-type stability for nonlinear fractional integro-differential equations have been studied in recent decades [5,7,[15][16][17].…”

“…Vu and Van Hoa [15] addressed the nonlinear IVP of the Volterra equations, and they used the successive approximation approach to explain the U-H and U-H-R stability of the following equations.…”