scholarly journals Generalized Fractional Integral Operators Involving Mittag-Leffler Function

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Hafte Amsalu ◽  
D. L. Suthar
Keyword(s):  
Fractional Integral ◽  
Special Functions ◽  
Integral Operators ◽  
General Nature ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

The aim of this paper is to study various properties of Mittag-Leffler (M-L) function. Here we establish two theorems which give the image of this M-L function under the generalized fractional integral operators involving Fox’s H-function as kernel. Corresponding assertions in terms of Euler, Mellin, Laplace, Whittaker, and K-transforms are also presented. On account of general nature of M-L function a number of results involving special functions can be obtained merely by giving particular values for the parameters.

scholarly journals Certain Properties of Generalized M-Series under Generalized Fractional Integral Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
D. L. Suthar ◽  
Fasil Gidaf ◽  
Mitku Andualem
Keyword(s):  
Laplace Transform ◽  
Fractional Integral ◽  
Special Functions ◽  
Integral Operators ◽  
General Nature ◽  
Transform Methods ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

The aim of this study is to introduce new (presumed) generalized fractional integral operators involving I -function as a kernel. In addition, two theorems have been developed under these operators that provide an image formula for this generalized M -series and also to study the different properties of the generalized M -series. The corresponding assertions in terms of Euler and Laplace transform methods are presented. Due to the general nature of the I -function and the generalized M -series, a number of results involving special functions can be achieved only by making appropriate values for the parameters.

scholarly journals On Extended General Mittag–Leffler Functions and Certain Inequalities

2019 ◽  
Vol 3 (2) ◽  
pp. 32
Author(s):  
Marcela V. Mihai ◽  
Muhammad Uzair Awan ◽  
Muhammad Aslam Noor ◽  
Tingsong Du ◽  
Artion Kashuri ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Function Of Two Variables ◽  
Generalized Fractional Integral Operators

In this paper, we introduce and investigate generalized fractional integral operators containing the new generalized Mittag–Leffler function of two variables. We establish several new refinements of Hermite–Hadamard-like inequalities via co-ordinated convex functions.

scholarly journals Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hendra Gunawan ◽  
Denny Ivanal Hakim ◽  
Yoshihiro Sawano ◽  
Idha Sihwaningrum
Keyword(s):  
Maximal Operator ◽  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Littlewood Maximal Operator ◽  
Generalized Fractional Integral Operators

We prove weak type inequalities for some integral operators, especially generalized fractional integral operators, on generalized Morrey spaces of nonhomogeneous type. The inequality for generalized fractional integral operators is proved by using two different techniques: one uses the Chebyshev inequality and some inequalities involving the modified Hardy-Littlewood maximal operator and the other uses a Hedberg type inequality and weak type inequalities for the modified Hardy-Littlewood maximal operator. Our results generalize the weak type inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces and extend to some singular integral operators. In addition, we also prove the boundedness of generalized fractional integral operators on generalized non-homogeneous Orlicz-Morrey spaces.

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