Finite time stability and relative controllability of Riemann‐Liouville fractional delay differential equations

2019 ◽  
Vol 42 (18) ◽  
pp. 6607-6623 ◽  
Author(s):  
Mengmeng Li ◽  
JinRong Wang
Keyword(s):  
Differential Equations ◽  
Finite Time ◽  
Delay Differential Equations ◽  
Time Stability ◽  
Relative Controllability ◽  
Finite Time Stability ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

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.

Numerical Simulation of Fractional Delay Differential Equations Using the Operational Matrix of Fractional Integration for Fractional-Order Taylor Basis

2021 ◽  
Vol 6 (1) ◽  
pp. 10
Author(s):  
İbrahim Avcı 
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Absolute Error ◽  
Algebraic Equations ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Taylor basis, is applied to solve these FDDEs. The main characteristic of this approach is, by utilizing the operational matrix of fractional integration, to reduce the given differential equation to a set of algebraic equations with unknown coefficients. This equation system can be solved efficiently using a computer algorithm. A bound on the error for the best approximation and fractional integration are also given. Several examples are given to illustrate the validity and applicability of the technique. The efficiency of the presented method is revealed by comparing results with some existing solutions, the findings of some other approaches from the literature and by plotting absolute error figures.

Sign in / Sign up

Export Citation Format

Share Document