scholarly journals On Generalized Fractional Integral Operators and the Generalized Gauss Hypergeometric Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dumitru Baleanu ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Integral Transform ◽  
Special Functions ◽  
Fractional Integration ◽  
Fractional Integral Operators ◽  
Integral Formulas ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

A remarkably large number of fractional integral formulas involving the number of special functions, have been investigated by many authors. Very recently, Agarwal (National Academy Science Letters) gave some integral transform and fractional integral formulas involving theFpα,β·. In this sequel, here, we aim to establish some image formulas by applying generalized operators of the fractional integration involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda. Some interesting special cases of our main results are also considered.

scholarly journals Certain Integral Transform and Fractional Integral Formulas for the Generalized Gauss Hypergeometric Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Integral Transform ◽  
Special Functions ◽  
Integral Transforms ◽  
Integral Formulas ◽  
Special Cases

A remarkably large number of integral transforms and fractional integral formulas involving various special functions have been investigated by many authors. Very recently, Agarwal gave some integral transforms and fractional integral formulas involving theFp(α,β)(·). In this sequel, using the same technique, we establish certain integral transforms and fractional integral formulas for the generalized Gauss hypergeometric functionsFp(α,β,m)(·). Some interesting special cases of our main results are also considered.

scholarly journals Pathway fractional integral operators of generalized k-wright function and k4-function

2017 ◽  
Vol 35 (2) ◽  
pp. 235 ◽  
Author(s):  
Dinesh Kumar ◽  
Ram Kishore Saxena ◽  
Jitendra Daiya
Keyword(s):  
Fractional Integral ◽  
Fractional Integration ◽  
Integral Operators ◽  
Wright Function ◽  
Finite Product ◽  
Fractional Integral Operators ◽  
Integral Formulas ◽  
Fractional Integration Operator ◽  
Composition Formula ◽  
Special Cases

In the present work we introduce a composition formula of the pathway fractional integration operator with finite product of generalized K-Wright function and K4-function. The obtained results are in terms of generalized Wright function.Certain special cases of the main results given here are also considered to correspond with some known and new (presumably) pathway fractional integral formulas.

scholarly journals Some new inequalities for generalized convex functions pertaining generalized fractional integral operators and their applications

2021 ◽  
Vol 17 (1) ◽  
pp. 37-64
Author(s):  
A. Kashuri ◽  
M.A. Ali ◽  
M. Abbas ◽  
M. Toseef
Keyword(s):  
Differentiable Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Generalized Convex Functions ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators ◽  
New Inequalities

Abstract In this paper, authors establish a new identity for a differentiable function using generic integral operators. By applying it, some new integral inequalities of trapezium, Ostrowski and Simpson type are obtained. Moreover, several special cases have been studied in detail. Finally, many useful applications have been found.

Fractional integral operators characterized by some new hypergeometric summation formulas

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Min-Jie Luo ◽  
Ravinder Krishna Raina
Keyword(s):  
Special Class ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Generalized Hypergeometric Functions ◽  
Fractional Integral Operators ◽  
Summation Formulas ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

AbstractThe purpose of this paper is to study generalized fractional integral operators whose kernels involve a very special class of generalized hypergeometric functions

scholarly journals Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 206 ◽  
Author(s):  
K.S. Nisar ◽  
D.L. Suthar ◽  
M. Bohra ◽  
S.D. Purohit
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Special Functions ◽  
Integral Operators ◽  
Factor X ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Mathieu Series ◽  
Srivastava’S Polynomials

Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral operators involving hypergeometric function in the kernel are applied to the product of Srivastava’s polynomials and the generalized Mathieu series, containing the factor x λ ( x k + c k ) − ρ in its argument. The results are expressed in terms of the generalized hypergeometric function and Hadamard product of the generalized Mathieu series. Corresponding special cases related to the Riemann–Liouville and Erdélyi–Kober fractional integral operators are also considered.

scholarly journals New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 122
Author(s):  
Ahmet Ocak Akdemir ◽  
Saad Ihsan Butt ◽  
Muhammad Nadeem ◽  
Maria Alessandra Ragusa
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
Integrable Functions ◽  
Inequality Theory ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Chebyshev's Inequality ◽  
Generalized Fractional Integral Operators

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have generalized many existing results as well as iterating the Chebyshev inequality in special cases.

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 Generalized Fractional Integral Operators andM-Series

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
A. M. Khan ◽  
R. K. Kumbhat ◽  
Amit Chouhan ◽  
Anita Alaria
Keyword(s):  
Hypergeometric Function ◽  
Numerical Computation ◽  
Power Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Generalized Hypergeometric Function ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

Two fractional integral operators associated with FoxH-function due to Saxena and Kumbhat are applied toM-series, which is an extension of both Mittag-Leffler function and generalized hypergeometric functionpFq. The Mellin and Whittaker transforms are obtained for these compositional operators withM-series. Further some interesting properties have been established including power function and Riemann-Liouville fractional integral operators. The results are expressed in terms ofH-function, which are in compact form suitable for numerical computation. Special cases of the results are also pointed out in the form of lemmas and corollaries.

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