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...

In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifica...

The present paper aims at the study and derivation of Saigo generalized fractional integral operator involving product of Hfunction of one variable and general class of polynomials. On account of the most general nature of the operator, H-function and general class of polynomials occurring in the main result, a large number of known and new results involving Rieman-Liouville, ErdélyiKober Fract...

We analyze the generalized time-dependent Schrödinger equation for the force free case, as a generalization, for example, of the standard time-dependent Schrödinger equation, time fractional Schrödinger equation, distributed order time fractional Schrödinger equation, and tempered in time Schrödinger equation. We relate it to the corresponding standard Schrödinger equation with effective potent...

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...

Let C be a category with strong monomorphic strong coimages, that is, every morphism ƒ of C factors as ƒ = u ° g so that g is a strong epimorphism and u is a strong monomorphism and this factorization is universal. We define the notion of strong Mittag-Leffler property in pro-C. We show that if ƒ : X → Y is a level morphism in pro-C such that ( ) p Y ! " is a strong epimorphism for all β > α, t...