Quantum calculus plays a significant role in many different branches such as quantum physics, hypergeometric series theory, and other physical phenomena. In our paper using quantitative calculus, we introduce new family of normalized analytic functions the open unit disk, which relates to both generalized Mittag–Leffler function Jackson differential operator. By subordination virtue, obtain som...

The purpose of this paper is to find new inclusion relations the harmonic class HF(ϱ,γ) with subclasses SHF*,KHF and TNHF(τ) functions by applying convolution operator Θ(ℑ) associated Mittag-Leffler function. Further for ϱ=0, several special cases main results are also obtained.

A novel method of an optimal summation is developed that allows for calculating from small-variable asymptotic expansions the characteristic amplitudes variables tending to infinity. The in two versions, as self-similar Borel–Leroy or Mittag–Leffler summations. It based on optimized iterated roots approximants applied and Mittag–Leffler- transformed series with subsequent inverse transformation...

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...