Marichev-Saigo-Maeda fractional integral operators involving the product of generalized Bessel -Maitland functions

2021 ◽  
Vol 39 (1) ◽  
pp. 95-105
Author(s):  
D. L. Suthar ◽  
Praveen Agarwal ◽  
Hafte Amsalu
Keyword(s):  
Fractional Integral ◽  
Fractional Integration ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Special Cases

The aim of this paper is to evaluate two theorems for fractional integration involving Appell’s function   due to Marichev-Saigo-Maeda, to the product of the generalized Bessel-Maitland function. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdẻlyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. Further, we point out also their relevance

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 Integral inequalities involving generalized Erdélyi-Kober fractional integral operators

2016 ◽  
Vol 14 (1) ◽  
pp. 89-99 ◽  
Author(s):  
Dumitru Baleanu ◽  
Sunil Dutt Purohit ◽  
Jyotindra C. Prajapati
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Weighted Version ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Chebyshev Functional

AbstractUsing the generalized Erdélyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional. The results given earlier by Purohit and Raina (2013) and Dahmani et al. (2011) are special cases of results obtained in present paper.

scholarly journals Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu-Bo Chen ◽  
Saima Rashid ◽  
Zakia Hammouch ◽  
Muhammad Aslam Noor ◽  
Rehana Ashraf ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Monotone Function ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Liouville Type ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral

AbstractWe establish certain new fractional integral inequalities involving the Raina function for monotonicity of functions that are used with some traditional and forthright inequalities. Taking into consideration the generalized fractional integral with respect to a monotone function, we derive the Grüss and certain other associated variants by using well-known integral inequalities such as Young, Lah–Ribarič, and Jensen integral inequalities. In the concluding section, we present several special cases of fractional integral inequalities involving generalized Riemann–Liouville, k-fractional, Hadamard fractional, Katugampola fractional, $(k,s)$ ( k , s ) -fractional, and Riemann–Liouville-type fractional integral operators. Moreover, we also propose their pertinence with other related known outcomes.

New integral inequalities for geometrically convex functions via conformable fractional integral operators

2021 ◽  
Vol 29 (2) ◽  
pp. 205-219 ◽  
Author(s):  
SAIMA RASHID ◽  
AHMET OCAK AKDEMIR ◽  
MUHAMMAD ASLAM NOOR ◽  
KHALIDA INAYAT NOOR
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Conformable Fractional Integral

We establish several basic inequalities versions of the Hermite-Hadamard type inequalities for GA− and GG−convexity for conformable fractional integrals. Several special cases are also discussed, which can be deduced from our main result.

scholarly journals New Chebyshev type inequalities via a general family of fractional integral operators with a modified Mittag-Leffler kernel

2021 ◽  
Vol 6 (10) ◽  
pp. 11167-11186
Author(s):  
Hari M. Srivastava ◽  
◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Abdullah M. Alsharif ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
General Family ◽  
Chebyshev Functional ◽  
Bounded Below

<abstract><p>The main goal of this article is first to introduce a new generalization of the fractional integral operators with a certain modified Mittag-Leffler kernel and then investigate the Chebyshev inequality via this general family of fractional integral operators. We improve our results and we investigate the Chebyshev inequality for more than two functions. We also derive some inequalities of this type for functions whose derivatives are bounded above and bounded below. In addition, we establish an estimate for the Chebyshev functional by using the new fractional integral operators. Finally, we find similar inequalities for some specialized fractional integrals keeping some of the earlier results in view.</p></abstract>

scholarly journals On Fractional Integral Inequalities Involving Hypergeometric Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
D. Baleanu ◽  
S. D. Purohit ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Gauss Hypergeometric Function ◽  
Liouville Type ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Chebyshev Functional

Here we aim at establishing certain new fractional integral inequalities involving the Gauss hypergeometric function for synchronous functions which are related to the Chebyshev functional. Several special cases as fractional integral inequalities involving Saigo, Erdélyi-Kober, and Riemann-Liouville type fractional integral operators are presented in the concluding section. Further, we also consider their relevance with other related known results.

scholarly journals Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
D. Baleanu ◽  
P. Agarwal ◽  
S. D. Purohit
Keyword(s):  
Bessel Function ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Integration ◽  
Fractional Integrals ◽  
General Character ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Generalized Bessel Functions ◽  
Special Cases

We apply generalized operators of fractional integration involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

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.

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.

Fractional powers of operators and Riesz fractional integrals

1989 ◽  
Vol 112 (3-4) ◽  
pp. 237-247 ◽  
Author(s):  
S. E. Schiavone
Keyword(s):  
Banach Spaces ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Fréchet Spaces ◽  
Test Functions ◽  
Fractional Powers ◽  
Fractional Integral Operators ◽  
Fractional Powers Of Operators

SynopsisIn this paper, a theory of fractional powers of operators due to Balakrishnan, which is valid for certain operators on Banach spaces, is extended to Fréchet spaces. The resultingtheory is shown to be more general than that developed in an earlier approach by Lamb, and is applied to obtain mapping properties of certain Riesz fractional integral operators on spaces of test functions.

Sign in / Sign up

Export Citation Format

Share Document