scholarly journals Some new inequalities for generalized fractional conformable integral operators

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Kottakkaran Sooppy Nisar ◽  
Gauhar Rahman ◽  
Aftab Khan
Keyword(s):  
Integral Operators ◽  
Integral Inequalities ◽  
Decreasing Functions ◽  
New Inequalities

Abstract The present paper aims to establish certain new classes of integral inequalities for a class of n ($n\in \mathbb{N}$ n ∈ N ) positive continuous and decreasing functions by utilizing the generalized fractional conformable integral operators (FCIO) recently defined by Khan and Khan. From these results, we also derive several particular cases.

scholarly journals On certain new CAUCHY–TYPE fracitioanl integral inequalities and OPIAL–TYPE fractional derivative inequalities

2015 ◽  
Vol 46 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Amit Chouhan
Keyword(s):  
Fractional Derivative ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Future Research ◽  
Cauchy Type ◽  
Fractional Integral Operators ◽  
Integrable Functions ◽  
New Inequalities

The aim of this paper is to establish several new fractional integral and derivative inequalities for non-negative and integrable functions. These inequalities related to the extension of general Cauchy type inequalities and involving Saigo, Riemann-Louville type fractional integral operators together with multiple Erdelyi-Kober operator. Furthermore the Opial-type fractional derivative inequality involving H-function is also established. The generosity of H-function could leads to several new inequalities that are of great interest of future research.

scholarly journals Some fractional proportional integral inequalities

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Gauhar Rahman ◽  
Thabet Abdeljawad ◽  
Aftab Khan ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Exponential Functions ◽  
Proportional Integral ◽  
Conformable Derivatives ◽  
Fractional Integrals And Derivatives ◽  
Decreasing Functions

Abstract In the last few years, various researchers studied the so-called conformable integrals and derivatives. Based on that notion some authors used modified conformable derivatives (proportional derivatives) to generate nonlocal fractional integrals and derivatives, called fractional proportional integrals and derivatives, which contain exponential functions in their kernels. Our aim in this paper is to establish some new integral inequalities by utilizing the fractional proportional-integral operators. In fact, certain new classes of integral inequalities for a class of n ($n\in \mathbb{N}$ n ∈ N ) positive continuous and decreasing functions on $[a,b]$ [ a , b ] are presented. The inequalities presented in this paper are more general than the existing classical inequalities.

scholarly journals On integral inequalities related to the weighted and the extended Chebyshev functionals involving different fractional operators

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Barış Çelik ◽  
Mustafa Ç. Gürbüz ◽  
M. Emin Özdemir ◽  
Erhan Set
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Fractional Integral Operators

AbstractThe role of fractional integral operators can be found as one of the best ways to generalize classical inequalities. In this paper, we use different fractional integral operators to produce some inequalities for the weighted and the extended Chebyshev functionals. The results are more general than the available classical results in the literature.

scholarly journals On some reverse integral inequalities

1990 ◽  
Vol 49 (2) ◽  
pp. 319-326 ◽  
Author(s):  
Luciana Nania
Keyword(s):  
Integral Inequalities ◽  
Reverse Inequality ◽  
Higher Integrability ◽  
Decreasing Functions

AbstractWe prove the higher integrability of nonnegative decreasing functions, verifying a reverse inequality, and we calculate the optimal integrability exponent for these functions.

scholarly journals Some New Tempered Fractional Pólya-Szegö and Chebyshev-Type Inequalities with Respect to Another Function

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad ◽  
Muhammad Samraiz
Keyword(s):  
Present Article ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Bounded Functions ◽  
New Inequalities

In this present article, we establish certain new Pólya–Szegö-type tempered fractional integral inequalities by considering the generalized tempered fractional integral concerning another function Ψ in the kernel. We then prove certain new Chebyshev-type tempered fractional integral inequalities for the said operator with the help of newly established Pólya–Szegö-type tempered fractional integral inequalities. Also, some new particular cases in the sense of classical tempered fractional integrals are discussed. Additionally, examples of constructing bounded functions are considered. Furthermore, one can easily form new inequalities for Katugampola fractional integrals, generalized Riemann–Liouville fractional integral concerning another function Ψ in the kernel, and generalized fractional conformable integral by applying different conditions.

scholarly journals Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1225 ◽  
Author(s):  
Saima Rashid ◽  
Fahd Jarad ◽  
Muhammad Aslam Noor ◽  
Humaira Kalsoom ◽  
Yu-Ming Chu
Keyword(s):  
Real World ◽  
Fractional Integral ◽  
Numerical Approximation ◽  
Integral Operators ◽  
Integral Inequalities ◽  
The Novel ◽  
Fractional Integral Operators ◽  
Real World Problems

In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Ψ . The authors prove several inequalities for newly defined GPF-integral with respect to another function Ψ . Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Ψ and the proportionality index ς . Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.

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 Inequalities for Strongly r-Convex Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Huriye Kadakal
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Special Cases ◽  
Class Of Functions ◽  
New Inequalities

In this study, firstly we introduce a new concept called “strongly r-convex function.” After that we establish Hermite-Hadamard-like inequalities for this class of functions. Moreover, by using an integral identity together with some well known integral inequalities, we establish several new inequalities for n-times differentiable strongly r-convex functions. In special cases, the results obtained coincide with the well-known results in the literature.

Sign in / Sign up

Export Citation Format

Share Document