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 …

Relative controllability of fractional delay differential equations via delayed perturbation of Mittag-Leffler functions

Z You, M Fečkan, JR Wang - Journal of Computational and Applied …, 2020 - Elsevier
This paper is concerned with the relative controllability of fractional delay systems in control
for finite dimensional spaces. A notion of fractional delay Grammian matrix involving two …

[PDF][PDF] Controllability of nonlinear delay oscillating systems

C Liang, JR Wang, D O'Regan - Electronic Journal of Qualitative …, 2017 - real.mtak.hu
In this paper, we study the controllability of a system governed by second order delay
differential equations. We introduce a delay Gramian matrix involving the delayed matrix …

Representation of solutions of nonhomogeneous conformable fractional delay differential equations

NI Mahmudov, M Aydın - Chaos, Solitons & Fractals, 2021 - Elsevier
This paper is about the conformable fractional delay equations. We offer a conformable
delay perturbation of matrix exponential function to give the representation of solutions for …

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

M Li, JR Wang - Mathematical Methods in the Applied Sciences, 2019 - Wiley Online Library
This paper firstly deals with finite time stability (FTS) of Riemann‐Liouville fractional delay
differential equations via giving a series of properties of delayed matrix function of Mittag …

Relative controllability in fractional differential equations with pure delay

M Li, A Debbouche, JR Wang - Mathematical methods in the …, 2018 - Wiley Online Library
In this paper, we study relative controllability of fractional differential equations with pure
delay. Delayed Gram‐type matrix criterion and rank criterion for relative controllability are …

[HTML][HTML] Representation of a solution for a fractional linear system with pure delay

C Liang, JR Wang, D O'Regan - Applied Mathematics Letters, 2018 - Elsevier
This paper gives a representation of a solution to the Cauchy problem for a fractional linear
system with pure delay. We introduce the fractional delayed matrices cosine and sine of a …

Multi-delayed perturbation of Mittag-Leffler type matrix functions

NI Mahmudov - Journal of Mathematical Analysis and Applications, 2022 - Elsevier
In this paper, we introduce a multivariate determining function and propose a multi-delayed
perturbation of Mittag-Leffler type matrix function. It is an extension of the classical Mittag …

Relative controllability of a stochastic system using fractional delayed sine and cosine matrices

JR Wang, T Sathiyaraj, D O'Regan - Nonlinear Analysis: Modelling …, 2021 - zurnalai.vu.lt
In this paper, we study the relative controllability of a fractional stochastic system with pure
delay in finite dimensional stochastic spaces. A set of sufficient conditions is obtained for …

Relative controllability of semilinear delay differential systems with linear parts defined by permutable matrices

JR Wang, Z Luo, M Fečkan - European Journal of Control, 2017 - Elsevier
This paper is devoted to analysis of relative controllability of semilinear delay differential
systems with linear parts defined by permutable matrices. By introducing a notion of delay …