The present paper deals with the study of a generalized Mittag-Leffler function and associated fractional operator. The operator has been discussed in the space of Lebesgue measurable functions. The composition with Riemann-Liouville fractional integration operator has been obtained.

The starting point of this paper are the Mittag–Leffler polynomials investigated in details by H. Bateman in [1]. Based on generalized integer powers of real numbers and deformed exponential function, we introduce deformed Mittag–Leffler polynomials defined by appropriate generating function. We investigate their recurrence relations, hypergeometric representation and orthogonality. Since they ...

In this paper, we show several Turán type inequalities for a generalized Mittag-Leffler function with four parameters via the [Formula: see text]-gamma function.

In this paper, the solution of a class of fractional Kinetic equation involving generalized I-function has been discussed. Special cases involving the Ifunction, H-function, generalized M-series, generalized Mittag-Leffler functions are also discussed. Results obtained are related to recent investigations of possible astrophysical solutions of the solar neutrino problem.

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.

The main object of this paper is to investigate the solution of the following free electron laser equations associated with generalized MittagLeffler function and a confluent hypergeometric function in two variables: Dα τ h(τ) = ω ∫ τ 0 t β−1 h(τ − t)E σ,β(iνt σ)dt+ δf(τ), where γ, δ, ω ∈ C; ν ∈ R,α > 0, σ > 0, β > 0; E σ,β(z) is the generalized Mittag-Leffler function and Dα τ h(τ) = λ Γ(γ) ∫ ...

Since Gösta Magus Mittag-Leffler introduced the so-called function in 1903 and studied its features five subsequent notes, passing first half of 20th century during which majority scientists remained almost unaware function, various extensions (referred to as type functions) have been researched applied a wide range problems physics, biology, chemistry, engineering. In context fractional calcul...

The aim of this work is to elaborate and define the idea refined convex function Raina type. In addition, we have attained some associated properties in manner newly introduced idea. To add more comprehension into investigated definition, obtain estimations Hermite-Hadamard inequality. For reader’s interest, remarks regarding Mittag-Leffer function. During last four decades, term Mitag-Leffler ...