In this paper, we consider an anti-periodic Boundary Value Problem for Volterra integro-differential equation of fractional order 1 < α ≤ 2, with generalized Mittag-Leffler function in the kernel. Some existence and uniqueness results are obtained by using some well known fixed point theorems. We give some examples to exhibit our results. c ©2016 All rights reserved.

Inspired by a number of recent investigations, we introduce the new analogues of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, the Apostol-Genocchi polynomials based on Mittag-Leffler function. Making use of the Caputo-fractional derivative, we derive some new interesting identities of these polynomials. It turns out that some known results are derived as special cases.

In this paper, we study the controllability of linear and nonlinear fractional damped dynamical systems, which involve fractional Caputo derivatives, with different order in finite dimensional spaces using the Mittag-Leffler matrix function and the iterative technique. A numerical example is provided to illustrate the theory.

In this paper a new function called as K-function, which is an extension of the generalization of the Mittag-Leffler function[10,11] and its generalized form introduced by Prabhakar[20], is introduced and studied by the author in terms of some special functions and derived the relations that exists between the Kfunction and the operators of Riemann-Liouville fractional integrals and derivatives.

In the present paper we obtain closed form solutions of spacetime fractional telegraph equations using Adomian decomposition method. The space and time fractional derivatives are considered as Caputo fractional derivative and the solutions are obtained in terms of Mittag-Leffler functions.

This is a survey paper illuminating the distinguished role of the Mittag-Leffler function and its generalizations in fractional analysis and fractional modeling. The content of the paper is connected to the recently published monograph by Rudolf Gorenflo, Anatoly Kilbas, Francesco Mainardi and Sergei Rogosin.

ABSTRACT In this paper, we employ the generalized fractional calculus operators on the generalized Mittag-Leffler function. Some results associated with generalized Wright function are obtained. Recent results of Chaurasia and Pandey are obtained as special cases. 2000 MATHEMATICS SUBJECT CLASSIFICATION 33C45, 47G20, 26A33.