This paper introduces a new fractional operator by using the concepts of q-calculus and q-Mittag-Leffler functions. With this operator, Janowski functions are generalized studied regarding their certain geometric characteristics. It also establishes solution complex Briot–Bouquet differential equation newly defined operator.

This paper studies the uniqueness of solutions for several generalized Abel’s integral equations and a related coupled system in Banach spaces. The results derived are new based on Babenko’s approach, Banach’s contraction principle multivariate Mittag–Leffler function. We also present some examples illustration our main theorems.

In this article we give a general prescription for incorporating memory effects in phase space kinetic equation, and consider in particular the generalized "fractional" relaxation time model equation. We solve this for small-signal charge carriers undergoing scattering, trapping, and detrapping in a time-of-flight experimental arrangement in two ways: (i) approximately via the Chapman-Enskog sc...

Abstract. This paper deals with the study of the generalized hypergeometric matrix function and obtains some of its properties. We rephrase some results from the previous (earlier) works that will be used in this study. We get the hypergeometric matrix function representation, matrix differential equation, generating matrix functions, bilinear generating matrix functions, matrix recurrence rela...

Integral representations, asymptotic behaviour and distribution of zeros for classical Mittag-Leeer functions as well as for the functions of Mittag-Leeer type are discussed. They are obtained by diierent approaches. Special attention is paid to the questions of growth regularity of these functions.

Special functions such as hypergeometric, zeta, Bessel, Whittaker, Struve, Airy, Weber-Hermite and Mittag-Leffler are obtained a solution to complex differential equations in engineering, science technology. In this work, generalized Euler-type integrals involving four parameters function proposed. Some special cases of type that corresponding well-known results the literature also inferred.

In this article, we obtain certain novel reverse Hölder- and Minkowski-type inequalities for modified unified generalized fractional integral operators (FIOs) with extended Mittag–Leffler functions (MLFs). The predominant results of article generalize extend the existing in literature. As applications, versions weighted Radon-, Jensen- power mean-type FIOs MLFs are also investigated.

The zero distribution of sections of Mittag–Leffler functions of order ρ > 1 was studied in 1983 by A. Edrei, E.B. Saff and R.S. Varga. In the present paper, we study the zero distribution of linear combinations of sections and tails of Mittag–Leffler functions of order ρ > 1.

A remarkably large number of unified integrals involving the Mittag–Leffler function have been presented. Here, with same technique as Choi and Agarwal, we propose establishment two generalized integral formulas a multivariate function, which are expressed in terms Lauricella series due to Srivastava Daoust. We also present some interesting special cases.

A new generalization of the Katugampola generalized fractional integrals in terms Mittag-Leffler functions is proposed. Consequently, generalizations Hermite-Hadamard inequalities by this newly proposed integral operator, for a positive convex stochastic process, are established. Other known results easily deduced as particular cases these inequalities. The obtained also hold any function.