Some fractional integral formulas for the Mittag-Leffler type function with four parameters

Abstract

Abstract:In this paper we present some results from the theory of fractional integration operators (of MarichevSaigo-Maeda type) involving the Mittag-Leffler type function with four parameters ; E ; OEz which has been recently introduced by Garg et al. Some interesting special cases are given to fractional integration operators involving some Special functions.

A New Generalization of Pochhammer Symbol and Its Applications

“…Proof. Using the integral representation given by (6) in the definition (9), we led to desired result (12).…”

Design of a Nonlinear Predictive Controller for a Fractional-Order Hydraulic Turbine Governing System with Mechanical Time Delay

“…Theorem 2. Considering the CARMA model (25) of a fractional-order HTGS (3), the system will converge to the reference trajectories Y r under the control law (26).…”

“…Nonlinear modeling and dynamic analysis of hydraulic turbine governing systems has always been a topic of interest, and there has been much research in this area [11][12][13][14][15][16][17]. There is a consensus that fractional calculus is superior to integer calculus in describing systems with memory, historical dependence, and viscoelasticity [18][19][20][21][22][23][24][25][26][27][28][29]. Considering the nonlinear, time-varying and nonminimum phase characteristics of hydraulic turbine governing systems, some scholars have introduced fractional calculus to establish mathematical models of HTGS which are more in line with engineering practice [30][31][32].…”

An Effect of the Environmental Pollution via Mathematical Model Involving the Mittag-Leffler Function

“…For the further details regarding above function we refer the book entitle "Mittag-Leffler functions, related topics and applications" by Gorenflo, Kilbas, Mainardi and Rogosin [7] (see, for examples [1,2,3] …”