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# A Generalizedq-Mittag-Leffler Function byq-Captuo Fractional Linear Equations

Abstract and Applied Analysis

Hindawi Limited

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### Abstract

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 (1995).

### Most cited references15

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### Initial value problems in discrete fractional calculus

(2009)
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### Discrete-Time Fractional Variational Problems

(2010)
We introduce a discrete-time fractional calculus of variations on the time scale $$h\mathbb{Z}$$, $$h > 0$$. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of the discrete-derivatives are integer values, and that they converge to the fractional continuous-time solutions when $$h$$ tends to zero. Our Legendre type condition is useful to eliminate false candidates identified via the Euler-Lagrange fractional equation.
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### Some Fractional q-Integrals and q-Derivatives

(1966)
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### Author and article information

###### Journal
Abstract and Applied Analysis
Abstract and Applied Analysis
Hindawi Limited
1085-3375
1687-0409
2012
2012
: 2012
:
: 1-11
10.1155/2012/546062