Stability for generalized Caputo proportional fractional delay integro-differential equations

Abstract

Abstract A scalar nonlinear integro-differential equation with time-variable and bounded delays and generalized Caputo proportional fractional derivative is considered. The main goal of this paper is to study the stability properties of the zero solution. Results are given concerning stability, exponential stability, asymptotic stability, and boundedness of solutions. The investigations are based on an application of a quadratic Lyapunov function, its generalized Caputo proportional derivative, and a modification of the Razumikhin approach. Some auxiliary properties of the generalized Caputo proportional derivative are proved. Five illustrative examples are included.

Keywords

• Generalized Caputo proportional fractional derivative
• Variable delays
• Integro-differential fractional equations
• Initial value problem