The main aim of this paper is to give refinement bounds fractional integral operators involving extended generalized Mittag-Leffler functions. A new definition, namely, strongly α , m -convex function introduced obtain improvements fo...

We consider some fractional extensions of the recursive differential equation governing the Poisson process, i.e. d d t pk(t) =−λ(pk(t)− pk−1(t)), k ≥ 0, t > 0 by introducing fractional time-derivatives of order ν , 2ν , ..., nν . We show that the so-called “Generalized Mittag-Leffler functions” Ek α,β(x), x ∈ R (introduced by Prabhakar [24]) arise as solutions of these equations. The correspon...

The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It shown that the derivative integral operators are bounded. Some fundamental characteristics of new operators, such as semi-group inverse characteristics, studied. As special cases these novel several already well known in literature acquired. generalized Laplace transform evaluated. By ...

The generalized exponential function in a complex domain is called the Mittag-Leffler (MLF). implementations of MLF are significant diverse areas science. Over past few decades, and its analysis with generalizations have become an increasingly rich research area mathematics allied fields. In geometric theory meromorphic functions, main contribution to this discipline study enrich operator on pu...

Abstract: Motivated by statistical mechanics contexts, we study the properties of the q-Laplace transform, which is an extension of the well-known Laplace transform. In many circumstances, the kernel function to evaluate certain integral forms has been studied. In this article, we establish relationships between q-exponential and other well-known functional forms, such as Mittag–Leffler functio...

In this paper, generalized versions of Hadamard and Fejér–Hadamard type fractional integral inequalities are obtained. By using integrals containing Mittag-Leffler functions, some well-known results for convex harmonically functions generalized. The paper connected with various published inequalities.

We show that data from recent experiments carried out on the kinetics of DNA escape from alpha-hemolysin nanopores [M. Wiggin, C. Tropini, C. T. Cossa, N. N. Jetha, and A. Marziali, Biophys. J. 95, 5317 (2008)] may be rationalized by a model of chain dynamics based on the anomalous diffusion of a particle moving in a harmonic well in the presence of a delta function sink. The experiments of Wig...