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...

By observing that the fractional Caputo derivative of order α ∈ (0, 1) can be expressed in terms a multiplicative convolution operator, we introduce and study class such operators which also have same self-similarity property as derivative. We proceed by identifying subclass is bijection with set Bernstein functions provide several representations their eigenfunctions, corresponding function, g...

*Correspondence: [email protected] 3Department of Mathematical Sciences, UAE University, Al Ain, United Arab Emirates Full list of author information is available at the end of the article Abstract In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involvin...

Abstract In this paper, we propose a generalized Gronwall inequality in the context of ψ -Hilfer proportional fractional derivative. Using Picard’s successive approximation and definition Mittag–Leffler functions, construct representation formula solution for differential equation with constant coefficient form kernel. The uniqueness result is proved by using Banach’s fixed-point theorem some p...

It has a wide application in the problem of physics, chemistry, biology, engineering and applied sciences. The theory Bessel functions is intimately connected with certain types differential equations. A detail account applications are given book Watson [26]. In this present paper, we establish generalized extension k-Bessel-Maitland function involving pathway integral operator. obtain composit...

We give a functorial characterization of Mittag-Leffler modules and strict Mittag-Leffler modules.

In this article, we study the Mittag-Leffler-Hyers-Ulam and Mittag-Leffler-Hyers-Ulam-Rassias stability of a class of fractional differential equation with boundary condition.

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...

Using the results of third-order differential subordination, we introduce certain families admissible functions and discuss some applications subordination for meromorphic associated with a linear operator containing generalized Mittag-Leffler function.