scholarly journals Generalized proportional fractional integral inequalities for convex functions

2021 ◽  
Vol 6 (10) ◽  
pp. 10765-10777
Author(s):  
Majid K. Neamah ◽  
◽  
Alawiah Ibrahim
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Special Values ◽  
Special Cases

<abstract><p>In this paper, we establish some inequalities for convex functions by applying the generalized proportional fractional integral. Some new results by using the linkage between the proportional fractional integral and the Riemann-Liouville fractional integral are obtained. Moreover, we give special cases of our reported results. Obtained results provide generalizations for some of the current results in the literature by applying some special values to the parameters.</p></abstract>

scholarly journals New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1753
Author(s):  
Saima Rashid ◽  
Aasma Khalid ◽  
Omar Bazighifan ◽  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Convex Mappings ◽  
Special Cases ◽  
Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

scholarly journals Tempered Fractional Integral Inequalities for Convex Functions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 500 ◽  
Author(s):  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Special Cases ◽  
New Inequalities

Certain new inequalities for convex functions by utilizing the tempered fractional integral are established in this paper. We also established some new results by employing the connections between the tempered fractional integral with the (R-L) fractional integral. Several special cases of the main result are also presented. The obtained results are more in a general form as it reduced certain existing results of Dahmani (2012) and Liu et al. (2009) by employing some particular values of the parameters.

scholarly journals General Raina fractional integral inequalities on coordinates of convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Badreddine Meftah
Keyword(s):  
Mathematical Model ◽  
Fractional Calculus ◽  
Convex Function ◽  
Mathematical Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Differentiable Functions ◽  
Special Cases

AbstractIntegral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized Raina fractional integral inequalities using an $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates. Also, we obtain an integral identity for partial differentiable functions. As an effect of this result, two interesting integral inequalities for the $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates are given. Finally, we can say that our findings recapture some recent results as special cases.

scholarly journals A Generalized Fejér-Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results

2018 ◽  
Author(s):  
Shin Min Kang ◽  
Ghulam Abbas ◽  
Ghulam Farid ◽  
Waqas Nazeer
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Hadamard Inequality ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Harmonically Convex Functions

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable &eta;-convex function. Moreover, our results include several new and known results as special cases.

scholarly journals Some new generalizations of Ostrowski type inequalities for s-convex functions via fractional integral operators

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5595-5609
Author(s):  
Erhan Set
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Present Note ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Class Of Functions

Remarkably a lot of Ostrowski type inequalities involving various fractional integral operators have been investigated by many authors. Recently, Raina [34] introduced a new generalization of the Riemann-Liouville fractional integral operator involving a class of functions defined formally by F? ?,?(x)=??,k=0 ?(k)/?(?k + ?)xk. Using this fractional integral operator, in the present note, we establish some new fractional integral inequalities of Ostrowski type whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville fractional integral operators.

scholarly journals Fractional Integral Inequalities of Hermite–Hadamard Type for Differentiable Generalized h-Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yingxia Yang ◽  
Muhammad Shoaib Saleem ◽  
Mamoona Ghafoor ◽  
Muhammad Imran Qureshi
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Special Cases

In the present paper, some fractional integral inequalities of Hermite–Hadamard type for functions whose derivatives are generalized h-convex are established. Moreover, several particular cases are also discussed which can be deduced from our results. As special cases, one can obtain several new versions of the results of generalized h-convexity for other various generalizations of convex functions.

scholarly journals Certain Fractional Proportional Integral Inequalities via Convex Functions

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 222 ◽  
Author(s):  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad ◽  
Samee Ullah
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Proportional Integral ◽  
Special Cases ◽  
Classical Integral

The goal of this article is to establish some fractional proportional integral inequalities for convex functions by employing proportional fractional integral operators. In addition, we establish some classical integral inequalities as the special cases of our main findings.

scholarly journals Some new fractional integral inequalities for exponentially m-convex functions via extended generalized Mittag-Leffler function

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saima Rashid ◽  
Farhat Safdar ◽  
Ahmet Ocak Akdemir ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Operator Inequalities ◽  
Special Cases

AbstractIn the article, we establish some new general fractional integral inequalities for exponentially m-convex functions involving an extended Mittag-Leffler function, provide several kinds of fractional integral operator inequalities and give certain special cases for our obtained results.

scholarly journals Inequalities for a Unified Integral Operator for Strongly α , m -Convex Function and Related Results in Fractional Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Chahn Yong Jung ◽  
Ghulam Farid ◽  
Kahkashan Mahreen ◽  
Soo Hak Shim
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Special Cases ◽  
Definition Of

In this paper, we study integral inequalities which will provide refinements of bounds of unified integral operators established for convex and α , m -convex functions. A new definition of function, namely, strongly α , m -convex function is applied in different forms and an extended Mittag-Leffler function is utilized to get the required results. Moreover, the obtained results in special cases give refinements of fractional integral inequalities published in this decade.

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.

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