Stability conditions for a mixed linear Levin–Nohel integrodifferential system

Asymptotic Behavior of Solutions in Nonlinear Neutral System with Two Volterra Terms

“…The matrix measure, with some conditions, was the key tool used to tackle these three types of stability for the system (3). The considered system contains two Volterra terms and a nonlinear term; hence, the obtained results generalise the findings of [19,23]. Our work is another example of the advantage of using the fixed-point method instead of the Lyapunov's method.…”

“…Many researchers studied the existence of solutions and asymptotic behavior of these equations; for example, in [9][10][11][12], the authors considered the exponential stability of continuous, discrete, and stochastic differential equations. In [13][14][15][16][17][18][19], the authors dealt with the existence and stability of one or n-dimensional equations.…”

“…In this context, the main contribution of this paper is to apply the Banach fixed-point theorem to the show stability, asymptotic stability and exponential stability of solutions for the system (3), which is the generalization of the papers [19,23]. The paper is organized as follows.…”