[HTML][HTML] Finite time stability of fractional delay differential equations

M Li, JR Wang - Applied Mathematics Letters, 2017 - Elsevier
In this paper, we firstly introduce a concept of delayed Mittag-Leffler type matrix function, an
extension of Mittag-Leffler matrix function for linear fractional ODEs, which help us to seek …

Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations

M Li, JR Wang - Applied Mathematics and Computation, 2018 - Elsevier
In this paper, we introduce a concept of delayed two parameters Mittag-Leffler type matrix
function, which is an extension of the classical Mittag-Leffler matrix function. With the help of …

Delayed perturbation of Mittag‐Leffler functions and their applications to fractional linear delay differential equations

NI Mahmudov - Mathematical Methods in the Applied Sciences, 2019 - Wiley Online Library
In this paper, we propose a delayed perturbation of Mittag‐Leffler type matrix function, which
is an extension of the classical Mittag‐Leffler type matrix function and delayed Mittag‐Leffler …

Ulam–Hyers–Mittag-Leffler stability of fractional-order delay differential equations

JR Wang, Y Zhang - Optimization, 2014 - Taylor & Francis
In this paper, we first prove two existence and uniqueness results for fractional-order delay
differential equation with respect to Chebyshev and Bielecki norms. Secondly, we prove the …

[HTML][HTML] Novel Mittag-Leffler stability of linear fractional delay difference equations with impulse

GC Wu, D Baleanu, LL Huang - Applied Mathematics Letters, 2018 - Elsevier
In this letter we propose a class of linear fractional difference equations with discrete-time
delay and impulse effects. The exact solutions are obtained by use of a discrete Mittag …

[HTML][HTML] Analytical and numerical methods for the stability analysis of linear fractional delay differential equations

E Kaslik, S Sivasundaram - Journal of Computational and Applied …, 2012 - Elsevier
In this paper, several analytical and numerical approaches are presented for the stability
analysis of linear fractional-order delay differential equations. The main focus of interest is …

Mittag‐Leffler Stability Theorem for Fractional Nonlinear Systems with Delay

SJ Sadati, D Baleanu, A Ranjbar… - Abstract and Applied …, 2010 - Wiley Online Library
Fractional calculus started to play an important role for analysis of the evolution of the
nonlinear dynamical systems which are important in various branches of science and …

Lyapunov method for nonlinear fractional differential systems with delay

Y Wen, XF Zhou, Z Zhang, S Liu - Nonlinear dynamics, 2015 - Springer
This paper deals with the stability of nonlinear fractional differential systems with delay.
Based on the Lyapunov functional method and the Lyapunov function method, respectively …

Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion

GC Wu, D Baleanu, SD Zeng - Communications in Nonlinear Science and …, 2018 - Elsevier
This study investigates finite-time stability of Caputo delta fractional difference equations. A
generalized Gronwall inequality is given on a finite time domain. A finite-time stability …

Stability analysis of linear fractional differential system with multiple time delays

W Deng, C Li, J Lü - Nonlinear Dynamics, 2007 - Springer
In this paper, we study the stability of n-dimensional linear fractional differential equation
with time delays, where the delay matrix is defined in (R+) n× n. By using the Laplace …