The model of population growth is revised in this paper. A new model is proposed based on the concept of fractional differentiation that uses the generalized Mittag-Leffler function as kernel of differentiation. The new model includes the choice of sexuality. The existence of unique solution is investigated and numerical solution is provided.

Abstract We develop a first-principles approach to define the communicability between two nodes in time-varying network with memory. The formulation is based on time-fractional Schrödinger equation, where fractional (of Caputo type) derivative accounts for memory of system. Using Hamiltonian tight-binding formalism we propose temporal as product Mittag-Leffer functions adjacency matrices snapsh...

Fractional inequalities are useful in establishing the uniqueness of solution for partial differential equations of fractional order. Also they provide upper and lower bounds for solutions of fractional boundary value problems. In this paper we obtain some general integral inequalities containing generalized Mittag-Leffler function and some already known integral inequalities have been produced...

In the paper, the authors generalize the notion “k-Mittag-Leffler function”, establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function. 1. Preliminaries Throughout this paper, let C, R, R0 , R, Z − 0 , and N denote respectively the sets of com...

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.

The present paper aims at the study and derivation of Saigo generalized fractional integral operator involving product of Hfunction of one variable and general class of polynomials. On account of the most general nature of the operator, H-function and general class of polynomials occurring in the main result, a large number of known and new results involving Rieman-Liouville, ErdélyiKober Fract...

The objective of this research is to obtain some fractional integral formulas concerning products the generalized Mittag–Leffler function and two H-functions. resulting are described in terms H-function several variables. Moreover, we give illustrative examples for efficiency general approach our results.

Using the results of third-order differential subordination, we introduce certain families admissible functions and discuss some applications subordination for meromorphic associated with a linear operator containing generalized Mittag-Leffler function.

This article aims to obtain inequalities containing the unified Mittag–Leffler function which give bounds of integral operators for a generalized convexity. These findings provide generalizations and refinements many inequalities. By setting values monotone functions, it is possible reproduce results classical convexities. The Hadamard-type several classes related convex functions are identifie...