Abstract
This paper is explored with the stability procedure for linear nonautonomous multiterm fractional damped systems involving time delay. Finite-time stability (FTS) criteria have been developed based on the extended form of Gronwall inequality. Also, the result is deduced to a linear autonomous case. Two examples of applications of stability analysis in numerical formulation are described showing the expertise of theoretical prediction.
Highlights
Fractional differential equations provide the outstanding device for account of remembrance and heritable characteristics of numerous complex systems
The Riemann–Liouville derivative cannot be used in the situation when the particular function is differentiable
Time delay occurs in the system subject to different causes such as communication delay, energy conversation, etc
Summary
Fractional differential equations provide the outstanding device for account of remembrance and heritable characteristics of numerous complex systems. The Gronwall inequality is known as Gronwall–Bellman inequality, which bounds the solution of given fractional system Due to this application, many researchers followed this inequality to analyze the existence of solution, stability related problems, oscillation and to check boundedness property of the given system. In [29], existence results for fractional-order damped systems are studied by using Holder and Gronwall inequalities. FTS of multiterm fractional-order damped dynamical system involving time delay has been studied. It is crucial to pay attention to check the FTS of linear nonautonomous multiterm fractional damped time delay system with order 0 < α2 1 < α1 2, which is examined by using extended form of generalized Gronwall’s inequality.
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