Hadamard type fractional time-delay semilinear differential equations: Delayed Mittag-Leffler function approach

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

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 type matrix function. With the help of the delayed perturbation of Mittag-Leffler type matrix function, we give an explicit formula of solutions to linear nonhomogeneous fractional delay differential equations.

A Quantum Generalized Mittag-Leffler Function Via Caputo q-Fractional Equations

Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler function is thought as the q-analogue of the one introduced previously by Kilbas and Saigo.

Caputo q-Fractional Initial Value Problems and a q-Analogue Mittag-Leffler Function

Caputo q-fractional derivatives are introduced and studied. A Caputo -type q-fractional initial value problem is solved and its solution is expressed by means of a new introduced q-Mittag-Leffler function. Some open problems about q-fractional integrals are proposed as well.

Mittag-Leffler Dichotomy and Roughness of Conformable Fractional Differential Equations

The solutions of traditional fractional differential equations neither satisfy group property nor generate dynamical systems, so the study on hyperbolicity is in blank. Relying on the new proposed conformable fractional derivative, we investigate dichotomy of conformable fractional equations, including structure of solutions of linear systems, Mittag-Leffler dichotomy and stability, roughness and nonuniform dichotomy.

Mittag-Leffler函数的离散延迟扰动及其在线性分数阶延迟差分系统中的应用

Discrete delayed perturbation of Mittag-Leffler function and its application to linear fractional delayed difference system

本文引入常系数线性非齐次分数阶差分系统，通过提出nabla Mittag-Leffler型函数的离散延迟扰动获得显式解，并讨论了相关特殊情况。

A natural extension of Mittag-Leffler function associated with a triple infinite series

We establish a new natural extension of Mittag-Leffler function with three variables which is so called "trivariate Mittag-Leffler function". The trivariate Mittag-Leffler function can be expressed via complex integral representation by putting to use of the eminent Hankel's integral. We also investigate Laplace integral relation and convolution result for a univariate version of this function. Moreover, we present fractional derivative of trivariate Mittag-Leffler function in Caputo type and we also discuss Riemann- Liouville type fractional integral and derivative of this function. The link …