Trivariate Mittag-Leffler functions used to solve multi-order systems of fractional differential equations

A Ahmadova, IT Huseynov, A Fernandez… - … in Nonlinear Science …, 2021 - Elsevier
Linear systems of fractional differential equations have been studied from various points of
view: applications to electric circuit theory, approximate solutions by numerical methods, and …

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 …

Explicit analytical solutions of incommensurate fractional differential equation systems

IT Huseynov, A Ahmadova, A Fernandez… - Applied Mathematics …, 2021 - Elsevier
Fractional differential equations have been studied due to their applications in modelling,
and solved using various mathematical methods. Systems of fractional differential equations …

Representation of solutions for linear fractional systems with pure delay and multiple delays

AM Elshenhab, XT Wang - Mathematical Methods in the …, 2021 - Wiley Online Library
Nonhomogeneous systems of linear fractional equations with pure delay and multiple
delays with linear parts given by permutable or nonpermutable matrices are considered …

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 …

Delayed analogue of three‐parameter Mittag‐Leffler functions and their applications to Caputo‐type fractional time delay differential equations

IT Huseynov, NI Mahmudov - Mathematical Methods in the …, 2020 - Wiley Online Library
In this paper, we consider a Cauchy problem for a Caputo‐type time delay linear system of
fractional differential equations with permutable matrices. First, we provide a new …

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 …

On a study for the neutral Caputo fractional multi-delayed differential equations with noncommutative coefficient matrices

M Aydin, NI Mahmudov - Chaos, Solitons & Fractals, 2022 - Elsevier
The representation of a solution to a neutral linear fractional multiple-delay differential
inhomogeneous system with non-commutative coefficient matrices is studied using a …

[HTML][HTML] Fractional Langevin type delay equations with two fractional derivatives

NI Mahmudov - Applied Mathematics Letters, 2020 - Elsevier
In this article, a delayed Mittag-Leffler type function is introduced. With the help of delayed
Mittag-Leffler type functions, we give an explicit solution formula to linear non-homogeneous …

[HTML][HTML] A class of Langevin time-delay differential equations with general fractional orders and their applications to vibration theory

IT Huseynov, NI Mahmudov - Journal of King Saud University-Science, 2021 - Elsevier
Langevin differential equations with fractional orders play a significant role due to their
applications in vibration theory, viscoelasticity and electrical circuits. In this paper, we mainly …