Stability to a Kind of Functional Differential Equations of Second Order with Multiple Delays by Fixed Points

Abstract

We discuss the stability of solutions to a kind of scalar Liénard type equations with multiple variable delays by means of the fixed point technique under an exponentially weighted metric. By this work, we improve some related results from one delay to multiple variable delays.

Stability in Functional Integro-differential Equations of Second Order with Variable Delay

“…Later, Pi [2,3] The author investigated the stability of the zero solution of this equation by means of the fixed point theory and an exponential weighted metric. In addition, for some related works on the qualitative behavior solutions of functional differential and integro-differential equations of the second order, we refer to the reader to the papers and books of Abdollahpour, et al [5], Ardjouni and Djoudi [6], Burton [7,8], Graef and Tunç [9], Hale [10], Jin and Luo [11], Korkmaz and Tunç [12], Levin and Nohel [13,14], Pi [15], Tunç and Biçer [16], Tunç [17], Tunç and Tunç [18], Zhao, et al [19], Zhao and Yuan [20] and the references therein.…”

Finite time stability of linear fractional order dynam-ical system with variable delays

“…Thus, there remain only geometric methods (Nyquist) which can be used for the stability check for bounded input bounded output. Different techniques have been proposed in the investigation of the stability for various fractional dynamical system, such as analytical approach [4], [27], fixed point theorem [9], [10], [51], the Lyapunov method [34], [35], linear matrix inequality [47], Gronwall inequality [12], [30]. Recently there have been advances in control theory of fractional order dynamical systems for different kinds of stability.…”