scholarly journals Fractional Integral Inequalities via Hadamard’s Fractional Integral

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Weerawat Sudsutad ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Integral Inequality ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Special Cases ◽  
Hadamard Fractional Integral

We establish new fractional integral inequalities, via Hadamard’s fractional integral. Several new integral inequalities are obtained, including a Grüss type Hadamard fractional integral inequality, by using Young and weighted AM-GM inequalities. Many special cases are also discussed.

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 On the weighted fractional Pólya–Szegö and Chebyshev-types integral inequalities concerning another function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Kottakkaran Sooppy Nisar ◽  
Gauhar Rahman ◽  
Dumitru Baleanu ◽  
Muhammad Samraiz ◽  
Sajid Iqbal
Keyword(s):  
Fractional Integral ◽  
Primary Objective ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Paper Cover ◽  
Special Cases ◽  
Type Integral ◽  
Bounded Functions ◽  
Conformable Fractional Integral ◽  
Hadamard Fractional Integral

Abstract The primary objective of this present paper is to establish certain new weighted fractional Pólya–Szegö and Chebyshev type integral inequalities by employing the generalized weighted fractional integral involving another function Ψ in the kernel. The inequalities presented in this paper cover some new inequalities involving all other type weighted fractional integrals by applying certain conditions on $\omega (\theta )$ ω ( θ ) and $\Psi (\theta )$ Ψ ( θ ) . Also, the Pólya–Szegö and Chebyshev type integral inequalities for all other type fractional integrals, such as the Katugampola fractional integrals, generalized Riemann–Liouville fractional integral, conformable fractional integral, and Hadamard fractional integral, are the special cases of our main results with certain choices of $\omega (\theta )$ ω ( θ ) and $\Psi (\theta )$ Ψ ( θ ) . Additionally, examples of constructing bounded functions are also presented in the paper.

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

scholarly journals Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Samaira Naz ◽  
Muhammad Nawaz Naeem ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Derivative Operator ◽  
Practical Applications ◽  
Mathematical Problems ◽  
Grüss Type Inequalities

AbstractIn this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions. For these functions, we develop some new fractional integral inequalities. Our results with this new derivative operator are capable of evaluating several mathematical problems relevant to practical applications.

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.

Some new fractional integral inequalities for generalized relative semi-m-(r; h1, h2)-preinvex mappings via generalized Mittag-Leffler function

2019 ◽  
Vol 26 (1/2) ◽  
pp. 41-55 ◽  
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Invex Set ◽  
Special Means ◽  
Special Cases ◽  
Differentiable Mappings

The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

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 New integral inequalities for strongly nonconvex functions involving Raina function

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2437-2456
Author(s):  
Artion Kashuri ◽  
Marcela Mihai ◽  
Muhammad Awan ◽  
Muhammad Noor ◽  
Khalida Noor
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Nonconvex Functions ◽  
Nonconvex Function ◽  
Special Cases ◽  
Type Integral ◽  
Generalized Fractional Integral ◽  
General Class Of Functions ◽  
Class Of Functions

In this paper, the authors defined a new general class of functions, the so-called strongly (h1,h2)-nonconvex function involving F??,?(?) (Raina function). Utilizing this, some Hermite-Hadamard type integral inequalities via generalized fractional integral operator are obtained. Some new results as a special cases are given as well.

scholarly journals Generalized Hadamard Fractional Integral Inequalities for Strongly s , m -Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Chao Miao ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Yanhua Bian
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Hadamard Fractional Integral

This article deals with Hadamard inequalities for strongly s , m -convex functions using generalized Riemann–Liouville fractional integrals. Several generalized fractional versions of the Hadamard inequality are presented; we also provide refinements of many known results which have been published in recent years.

scholarly journals Some integral inequalities for approximately h—convex functions and their applications

2021 ◽  
Vol 40 (2) ◽  
pp. 481-504
Author(s):  
Artion Kashuri ◽  
Muhammad Raees ◽  
Matloob Anwar
Keyword(s):  
Convex Function ◽  
Integral Inequality ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Integral Type ◽  
Special Cases ◽  
Hölder’S Integral Inequality ◽  
Error Estimations

In this paper, by applying the new and improved form of Hölder’s integral inequality called Hölder—Íşcan integral inequality three inequalities of Hermite—Hadamard and Hadamard integral type for (h, d)—convex functions have been established. Various special cases including classes for instance, h—convex, s—convex function of Breckner and Godunova—Levin—Dragomir and strong versions of the aforementioned types of convex functions have been identified. Some applications to error estimations of presented results have been analyzed. At the end, a briefly conclusion is given.

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