Matrix Mittag-Leffler functions of fractional nabla calculus

author

  • Jagan Mohan Jonnalagadda Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad-500078, Telangana, India
Abstract:

In this article, we propose the definition of one parameter matrix Mittag-Leffler functions of fractional nabla calculus and present three different algorithms to construct them. Examples are provided to illustrate the applicability of suggested algorithms.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

On certain fractional calculus operators involving generalized Mittag-Leffler function

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...

full text

Fractional Calculus of the Generalized Mittag-Leffler Type Function

We introduce and study a new function called R-function, which is an extension of the generalized Mittag-Leffler function. We derive the relations that exist between the R-function and Saigo fractional calculus operators. Some results derived by Samko et al. (1993), Kilbas (2005), Kilbas and Saigo (1995), and Sharma and Jain (2009) are special cases of the main results derived in this paper.

full text

Fractional integral operators and the multiindex Mittag-Leffler functions

The aim of this paper is to study some properties of multiindex Mittag-Leffler type function E(1/ρj),(μj)(z) introduced by Kiryakova [V. Kiryakova, J. Comput. Appl. Math. 118 (2000), 241-259]. Here we establish certain theorems which provide the image of this function under the Saigo’s fractional integral operators. The results derived are of general character and give rise to a number of known...

full text

on certain fractional calculus operators involving generalized mittag-leffler function

the object of this paper is to establish certain generalized fractional integration and differentiation involving generalized mittag-leffler function defined by salim and faraj [25]. the considered generalized fractional calculus operators contain the appell's function $f_3$ [2, p.224] as kernel and are introduced by saigo and maeda [23]. the marichev-saigo-maeda fractional calculus operat...

full text

Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations

and Applied Analysis 3 and define recursively a∇−nf t ∫ t a a∇−n 1f τ ∇τ 2.4 for n 2, 3, . . .. Then we have the following. Proposition 2.1 Nabla Cauchy formula . Let n ∈ Z , a, b ∈ T and let f : T → R be ∇-integrable on a, b ∩ T. If t ∈ T, a ≤ t ≤ b, then a∇−nf t ∫ t a ̂ hn−1 ( t, ρ τ ) f τ ∇τ . 2.5 Proof. This assertion can be proved by induction. If n 1, then 2.5 obviously holds. Let n ≥ 2 an...

full text

Nabla discrete fractional calculus and nabla inequalities

Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincaré and Sobolev type inequalities .

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 6  issue 2

pages  128- 140

publication date 2018-04-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023