scholarly journals Certain Hadamard Proportional Fractional Integral Inequalities

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 504 ◽  
Author(s):  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Integral Operator ◽  
Difference Equations ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Exponential Functions ◽  
Non Local ◽  
Positive Functions

In this present paper we study the non-local Hadmard proportional integrals recently proposed by Rahman et al. (Advances in Difference Equations, (2019) 2019:454) which containing exponential functions in their kernels. Then we establish certain new weighted fractional integral inequalities involving a family of n ( n ∈ N ) positive functions by utilizing Hadamard proportional fractional integral operator. The inequalities presented in this paper are more general than the inequalities existing in the literature.

scholarly journals On Some Fractional Integral Inequalities Involving Caputo–Fabrizio Integral Operator

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 255
Author(s):  
Vaijanath L. Chinchane ◽  
Asha B. Nale ◽  
Satish K. Panchal ◽  
Christophe Chesneau
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Chebyshev Functional ◽  
Positive Functions

In this paper, we deal with the Caputo–Fabrizio fractional integral operator with a nonsingular kernel and establish some new integral inequalities for the Chebyshev functional in the case of synchronous function by employing the fractional integral. Moreover, several fractional integral inequalities for extended Chebyshev functional by considering the Caputo–Fabrizio fractional integral operator are discussed. In addition, we obtain fractional integral inequalities for three positive functions involving the same operator.

scholarly journals Generalized proportional fractional integral functional bounds in Minkowski’s inequalities

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tariq A. Aljaaidi ◽  
Deepak B. Pachpatte ◽  
Wasfi Shatanawi ◽  
Mohammed S. Abdo ◽  
Kamaleldin Abodayeh
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Functional ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Special Cases ◽  
Close Relationship ◽  
Open Issue ◽  
Conclusion Section ◽  
Positive Functions

AbstractIn this research paper, we improve some fractional integral inequalities of Minkowski-type. Precisely, we use a proportional fractional integral operator with respect to another strictly increasing continuous function ψ. The functions used in this work are bounded by two positive functions to get reverse Minkowski inequalities in a new sense. Moreover, we introduce new fractional integral inequalities which have a close relationship to the reverse Minkowski-type inequalities via ψ-proportional fractional integral, then with the help of this fractional integral operator, we discuss some new special cases of reverse Minkowski-type inequalities through this work. An open issue is covered in the conclusion section to extend the current findings to be more general.

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 Some estimations on continuous random variables for (k, s) −fractional integral operators

2020 ◽  
Vol 6 (1) ◽  
pp. 143-154
Author(s):  
Mohamed Houas
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Random Variables ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integral Operators

AbstractIn this work, we establish some new (k, s) −fractional integral inequalities of continuous random variables by using the (k, s) −Riemann-Liouville fractional integral operator.

scholarly journals New Hadamard-type inequalities via $(s,m_{1},m_{2})$-convex functions

2021 ◽  
Vol 31 (4) ◽  
pp. 597-612
Author(s):  
B. Bayraktar ◽  
S.I. Butt ◽  
Sh. Shaokat ◽  
J.E. Nápoles Valdés
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Class Of Functions

The article introduces a new concept of convexity of a function: $(s,m_{1},m_{2})$-convex functions. This class of functions combines a number of convexity types found in the literature. Some properties of $(s,m_{1},m_{2})$-convexities are established and simple examples of functions belonging to this class are given. On the basis of the proved identity, new integral inequalities of the Hadamard type are obtained in terms of the fractional integral operator. It is shown that these results give us, in particular, generalizations of a number of results available in the literature.

scholarly journals Fractional integral inequalities involving Marichev–Saigo–Maeda fractional integral operator

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Asifa Tassaddiq ◽  
Aftab Khan ◽  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Moheb Saad Abouzaid ◽  
...  
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Inequalities

scholarly journals New Hadamard-type inequalities via $(s,m_{1},m_{2})$-convex functions

2021 ◽  
Vol 31 (4) ◽  
pp. 597-612
Author(s):  
B. Bayraktar ◽  
S.I. Butt ◽  
Sh. Shaokat ◽  
J.E. Napoles Valdes
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Class Of Functions

The article introduces a new concept of convexity of a function: $(s,m_{1},m_{2})$-convex functions. This class of functions combines a number of convexity types found in the literature. Some properties of $(s,m_{1},m_{2})$-convexities are established and simple examples of functions belonging to this class are given. On the basis of the proved identity, new integral inequalities of the Hadamard type are obtained in terms of the fractional integral operator. It is shown that these results give us, in particular, generalizations of a number of results available in the literature.

scholarly journals Certain new weighted estimates proposing generalized proportional fractional operator in another sense

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Thabet Abdeljawad ◽  
Saima Rashid ◽  
A. A. El-Deeb ◽  
Zakia Hammouch ◽  
Yu-Ming Chu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Mathematical Physics ◽  
Fractional Integral Operator ◽  
Fractional Operator ◽  
Weighted Estimates ◽  
Fractional Differential ◽  
Positive Functions ◽  
Katugampola Fractional Integral ◽  
Hadamard Fractional Integral

Abstract The present work investigates the applicability and effectiveness of generalized proportional fractional integral ($\mathcal{GPFI}$ GPFI ) operator in another sense. We aim to derive novel weighted generalizations involving a family of positive functions n ($n\in \mathbb{N}$ n ∈ N ) for this recently proposed operator. As applications of this operator, we can generate notable outcomes for Riemann–Liouville ($\mathcal{RL}$ RL ) fractional, generalized $\mathcal{RL}$ RL -fractional operator, conformable fractional operator, Katugampola fractional integral operator, and Hadamard fractional integral operator by changing the domain. The proposed strategy is vivid, explicit, and it can be used to derive new solutions for various fractional differential equations applied in mathematical physics. Certain remarkable consequences of the main theorems are also figured.

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 η-convex function. Moreover, our results include several new and known results as special cases.

scholarly journals Reverse Hermite-Hadamard's inequalities using \(\psi \)-fractional integral

2020 ◽  
Vol 3 (4) ◽  
pp. 75-84
Author(s):  
Tariq A. Aljaaidi ◽  
◽  
Deepak B. Pachpatte ◽  
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Concave Functions ◽  
Increasing Function

Our purpose in this paper is to use \(\psi-\)Riemann-Liouville fractional integral operator which is the fractional integral of any function with respect to another increasing function to establish some new fractional integral inequalities of Hermite-Hadamard, involving concave functions. Using the concave functions, we establish some new fractional integral inequalities related to the Hermite-Hadamard type inequalities via \(\psi-\)Riemann-Liouville fractional integral operator.

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