Existence and finite-time stability results for impulsive fractional differential equations with maxima

2015 ◽  
Vol 51 (1-2) ◽  
pp. 67-79 ◽  
Author(s):  
Yuruo Zhang ◽  
JinRong Wang
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Finite Time ◽  
Time Stability ◽  
Finite Time Stability ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential ◽  
Stability Results

New finite-time stability analysis of singular fractional differential equations with time-varying delay

2020 ◽  
Vol 23 (2) ◽  
pp. 504-519 ◽  
Author(s):  
Nguyen T. Thanh ◽  
Vu N. Phat ◽  
Piyapong Niamsup
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Finite Time ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
Varying Delay

AbstractThe Lyapunov function method is a powerful tool to stability analysis of functional differential equations. However, this method is not effectively applied for fractional differential equations with delay, since the constructing Lyapunov-Krasovskii function and calculating its fractional derivative are still difficult. In this paper, to overcome this difficulty we propose an analytical approach, which is based on the Laplace transform and “inf-sup” method, to study finite-time stability of singular fractional differential equations with interval time-varying delay. Based on the proposed approach, new delay-dependent sufficient conditions such that the system is regular, impulse-free and finite-time stable are developed in terms of a tractable linear matrix inequality and the Mittag-Leffler function. A numerical example is given to illustrate the application of the proposed stability conditions.

scholarly journals Scalar linear impulsive Riemann-Liouville fractional differential equations with constant delay-explicit solutions and finite time stability

2020 ◽  
Vol 53 (1) ◽  
pp. 121-130 ◽  
Author(s):  
Snezhana G. Hristova ◽  
Stepan A. Tersian
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Lower Limit ◽  
Fractional Differential Equations ◽  
Finite Time ◽  
Explicit Solutions ◽  
Time Stability ◽  
Constant Delay ◽  
Finite Time Stability ◽  
Fractional Differential

AbstractRiemann-Liouville fractional differential equations with a constant delay and impulses are studied in this article. The following two cases are considered: the case when the lower limit of the fractional derivative is fixed on the whole interval of consideration and the case when the lower limit of the fractional derivative is changed at any point of impulse. The initial conditions as well as impulsive conditions are defined in an appropriate way for both cases. The explicit solutions are obtained and applied to the study of finite time stability.

Finite-Time Stability of Hadamard Fractional Differential Equations in Weighted Banach Spaces

2021 ◽  
Author(s):  
Li Ma ◽  
Bowen Wu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Finite Time ◽  
Matrix Function ◽  
Time Stability ◽  
Weakly Singular Kernel ◽  
Finite Time Stability ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential ◽  
Pure Delay

Abstract The main purpose of this paper is to investigate the finite-time stability of Hadamard fractional differential equations (HFDEs). Firstly, the standard definition of finite-time stability of HFDEs in compatible Banach space are proposed. In light of the method of successive approximation and Beesack inequality with weakly singular kernel, the criteria for finite-time stability of linear and nonlinear HFDEs are established, respectively. Then with regard to linear HFDEs with pure delay, a novel fractional delayed matrix function (also called delayed Mittag-Leffler matrix function) is given. Specific to nonlinear HFDEs with constant time delay, both Beesack inequality and Hölder inequality are utilized in the framework of the generalized Lipschitz condition. Finally, several indispensable simulations are implemented to verify the effectiveness and practicability of the main results.

Periodic impulsive fractional differential equations

2017 ◽  
Vol 8 (1) ◽  
pp. 482-496 ◽  
Author(s):  
Michal Fečkan ◽  
Jin Rong Wang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Fractional Differential Equations ◽  
Periodic Boundary ◽  
Lorenz System ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential ◽  
Existence Of Periodic Solutions ◽  
Lower Limits ◽  
Stability Results

Abstract This paper deals with the existence of periodic solutions of fractional differential equations with periodic impulses. The first part of the paper is devoted to the uniqueness, existence and asymptotic stability results for periodic solutions of impulsive fractional differential equations with varying lower limits for standard nonlinear cases as well as for cases of weak nonlinearities, equidistant and periodically shifted impulses. We also apply our result to an impulsive fractional Lorenz system. The second part extends the study to periodic impulsive fractional differential equations with fixed lower limit. We show that in general, there are no solutions with long periodic boundary value conditions for the case of bounded nonlinearities.

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