scholarly journals On the Novel Finite-Time Stability Results for Uncertain Fractional Delay Differential Equations Involving Noninstantaneous Impulses

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Qien Li ◽  
Danfeng Luo ◽  
Zhiguo Luo ◽  
Quanxin Zhu
Keyword(s):  
Differential Equations ◽  
Finite Time ◽  
Delay Differential Equations ◽  
The Novel ◽  
Time Stability ◽  
Finite Time Stability ◽  
Fractional Delay ◽  
Delay Differential ◽  
Noninstantaneous Impulses ◽  
Stability Results

In this paper, we mainly study the finite-time stability for a kind of uncertain fractional-order delay differential equations with noninstantaneous impulses. By using the Lyapunov functions along with the generalized Grönwall inequality, we present the new stability results for the considered equations. Finally, two examples are given to demonstrate the effectiveness of our theoretical results.

An Extended Predictor–Corrector Algorithm for Variable-Order Fractional Delay Differential Equations

2016 ◽  
Vol 11 (6) ◽  
Author(s):  
B. Parsa Moghaddam ◽  
Sh. Yaghoobi ◽  
J. A. Tenreiro Machado
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Fractional Derivatives ◽  
Variable Order ◽  
The Novel ◽  
Fractional Delay ◽  
Novel Method ◽  
Delay Differential ◽  
Predictor Corrector ◽  
Fractional Delay Differential Equations

This article presents a numerical method based on the Adams–Bashforth–Moulton scheme to solve variable-order fractional delay differential equations (VFDDEs). In these equations, the variable-order (VO) fractional derivatives are described in the Caputo sense. The existence and uniqueness of the solutions are proved under Lipschitz condition. Numerical examples are presented showing the applicability and efficiency of the novel method.

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