scholarly journals Generalizations of Hardy’s Type Inequalities via Conformable Calculus

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 242
Author(s):  
Ghada AlNemer ◽  
Mohammed Kenawy ◽  
Mohammed Zakarya ◽  
Clemente Cesarano ◽  
Haytham M. Rezk
Keyword(s):  
Fractional Calculus ◽  
Integral Inequalities ◽  
Special Cases ◽  
Classical Integral ◽  
Conformable Calculus

In this paper, we derive some new fractional extensions of Hardy’s type inequalities. The corresponding reverse relations are also obtained by using the conformable fractional calculus from which the classical integral inequalities are deduced as special cases at α=1.

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 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 Opial and Pólya Type Inequalities Via Convexity

2018 ◽  
Vol 60 (1) ◽  
pp. 145-159 ◽  
Author(s):  
S. H. Saker ◽  
D. M. Abdou ◽  
I. Kubiaczyk
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Hölder’S Inequality ◽  
Jensen’S Inequality ◽  
Chain Rule ◽  
Integral Inequalities ◽  
Taylor Formula ◽  
Special Cases ◽  
Discrete Inequalities ◽  
Classical Integral

Abstract In this paper, we prove some new dynamic inequalities related to Opial and Pólya type inequalities on a time scale 𝕋. We will derive the integral and discrete inequalities of Pólya’s type as special cases and also derive several classical integral inequalities of Opial’s type that has been obtained in the literature as special cases. The main results will be proved by using the chain rule, Hölder’s inequality and Jensen’s inequality, Taylor formula on time scales.

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.

A note on fractional integral operator associated with multiindex Mittag-Leffler functions

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1931-1939 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Fractional Integral ◽  
Fractional Integration ◽  
Fractional Integral Operator ◽  
Integration Formula ◽  
Special Cases

Recently Kiryakova and several other ones have investigated so-called multiindex Mittag-Leffler functions associated with fractional calculus. Here, in this paper, we aim at establishing a new fractional integration formula (of pathway type) involving the generalized multiindex Mittag-Leffler function E?,k[(?j,?j)m;z]. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

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 Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

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 Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications

2020 ◽  
Vol 10 (2) ◽  
pp. 226-236
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Trapezium Type ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Preinvex Functions ◽  
Almost All

Trapezoidal inequalities for functions of divers natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means have been analyzed. The ideas and techniques of this paper may stimulate further research.

scholarly journals Some new generalizations of Maroni inequality on time scales

2013 ◽  
Vol 46 (4) ◽  
Author(s):  
Li Yin ◽  
Changjian Zhao
Keyword(s):  
Time Scales ◽  
Integral Inequalities ◽  
Special Cases

AbstractThe aim of present paper is to establish some new integral inequalities on time scales involving several functions and their derivatives which in the special cases yield the well known Maroni inequality and some of its generalizations.

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