# Theorem for Series in Three-Parameter Mittag-Leffler Function

@article{Soubhia2010TheoremFS, title={Theorem for Series in Three-Parameter Mittag-Leffler Function}, author={Ana Luisa Soubhia and Rubens de Figueiredo Camargo and E. Capelas De Oliveira and J. Jr. Vaz}, journal={Fractional Calculus and Applied Analysis}, year={2010}, volume={13}, pages={9-20} }

The new result presented here is a theorem involving series in the threeparameter Mittag-Le†er function. As a by-product, we recover some known results and discuss corollaries. As an application, we obtain the solution of a fractional difierential equation associated with a RLC electrical circuit in a closed form, in terms of the two-parameter Mittag-Le†er function.

## 29 Citations

### On a sum with a three-parameter Mittag-Leffler function

- Mathematics
- 2016

ABSTRACT The bounding of the two-parameter Mittag-Leffler function is discussed. As a particular consequence, we present two proofs for a sum involving a three-parameter Mittag-Leffler function. This…

### On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

- Mathematics
- 2012

The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations. The so-called generalized…

### A new generalization of Mittag-Leffler function via q-calculus

- Mathematics
- 2020

The present paper deals with a new different generalization of the Mittag-Leffler function through q -calculus. We then investigate its remarkable properties like convergence, recurrence relation,…

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

- Mathematics
- 2020

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…

### The extended Mittag-Leffler function and its properties

- Mathematics
- 2014

In this paper, we present the extended Mittag-Leffler functions by using the extended Beta functions (Chaudhry et al. in Appl. Math. Comput. 159:589-602, 2004) and obtain some integral…

### Analytical properties of (q, k)-Mittag Leffler function

- Mathematics
- 2019

This article is refer to the study of q analogue, which play significant role in number theory and combinatorics of annihilation. Here, we aim to presenting a new definition of (q,k)-Mittag Leffler…

### New approach to generalized Mittag-Leffler function via quantum calculus

- Mathematics
- 2019

We aim to introduce a new extension of Mittag-Leffler function via q-analogue and obtained their significant properties including integral representation, q-differentiation, q-Laplace transform,…

### Euler type integral operator involving k-Mittag-Leffler function

- MathematicsBoletim da Sociedade Paranaense de Matemática
- 2019

This paper deals with a Euler type integral operator involving k-Mittag-Leffler function defined by Gupta and Parihar [8]. Furthermore, some special cases are also taken into consideration.

### Application of Sumudu Transform in Fractional Differential Equation Associated with RLC Electrical Circuit

- Mathematics
- 2010

In this paper, we obtain the solution of a fractional differential equation associated with a RLC electrical circuit. The solution is derived by the application of the Sumudu transform. The results…

### An Application of Fractional Calculus in Electrical Engineering

- Mathematics
- 2016

In this paper, we use the Caputo fractional differential operator, which is introduced by Italian scientist Caputo in 1967, an attempt as an application in electrical engineering, we obtain the…

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