Finite-time stability of linear stochastic fractional-order systems with time delay

This paper focuses on the finite-time stability of linear stochastic fractional-order systems with time delay for $\alpha \in (\frac{1}{2},1)$ α ∈ ( 1 2 , 1 ) . Under the generalized Gronwall inequality and stochastic analysis techniques, the finite-time stability of the solution for linear stochastic fractional-order systems with time delay is investigated. We give two illustrative examples to show the interest of the main results.

Existence of solutions for fractional differential inclusions with initial value condition and non-instantaneous impulses

In this paper, we mainly consider the existence of solutions for a kind of ?-Hilfer fractional differential inclusions involving non-instantaneous impulses. Utilizing another nonlinear alternative of Leray-Schauder type, we present a new constructive result for the addressed system with the help of generalized Gronwall inequality and Lagrange mean-value theorem, and some achievements in the literature can be generalized and improved. As an application, a typical example is delineated to demonstrate the effectiveness of our theoretical results.

A generalized discrete fractional Gronwall inequality and its application on the uniqueness of solutions for nonlinear delay fractional difference system

In this paper, we state and prove a new discrete fractional version of the generalized Gronwall inequality. Based on this, a particular version expressed by means of discrete Mittag-Leer functions is provided. As an application, we prove the uniqueness and obtain an estimate for the solutions of nonlinear delay Caputo fractional difference system. Numerical example is presented to demonstrate the applicability of the main results.

Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality

This paper studies the finite-time stability of neutral fractional time-delay systems. With the generalized Gronwall inequality, sufficient conditions of the finite-time stability are obtained for the particular class of neutral fractional time-delay systems.

Finite-Time Stability of Fractional-Order BAM Neural Networks with Distributed Delay

Based on the theory of fractional calculus, the generalized Gronwall inequality and estimates of mittag-Leffer functions, the finite-time stability of Caputo fractional-order BAM neural networks with distributed delay is investigated in this paper. An illustrative example is also given to demonstrate the effectiveness of the obtained result.