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.

This paper is based upon incomplete fractional calculus and with the help of this, derived fractionalcalculus formula for Mittag-Leffler function. The results obtained are found in form ofincomplete Wright function hypergeometric

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.

The paper is devoted to study analogues of the van der Corput lemmas involving Mittag-Leffler functions. generalisation that we replace exponential function with Mittag-Leffler-type function, oscillatory integrals appearing in analysis time-fractional partial differential equations. More specifically, integral form I?,?(?)=?RE?,?(i???(x))?(x)dx, for range 00. This extends variety estimat...

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...