scholarly journals A GRÜSS TYPE INTEGRAL INEQUALITY ASSOCIATED WITH GAUSS HYPERGEOMETRIC FUNCTION FRACTIONAL INTEGRAL OPERATOR

2015 ◽  
Vol 30 (2) ◽  
pp. 81-92 ◽  
Author(s):  
Junesang Choi ◽  
Sunil Dutt Purohit
Keyword(s):  
Integral Operator ◽  
Hypergeometric Function ◽  
Integral Inequality ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Gauss Hypergeometric Function ◽  
Type Integral

scholarly journals New Approach to Minkowski Fractional Inequalities Using Generalized K-fractional Integral Operator

2018 ◽  
Vol 85 (1-2) ◽  
pp. 32
Author(s):  
Vaijanath L. Chinchane
Keyword(s):  
Integral Operator ◽  
Hypergeometric Function ◽  
Integral Inequality ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Gauss Hypergeometric Function ◽  
New Approach

In this paper, we obtain results related to Minkowski fractional integral inequality using generalized k-fractional integral operator is in terms of the Gauss hypergeometric function.

Generalized Minkowski-type Fractional Inequalities Involving Extended Mittag-leffler Function

2020 ◽  
Vol 87 (3-4) ◽  
pp. 137
Author(s):  
Maja Andrić ◽  
Ghulam Farid ◽  
Josip Pećarić ◽  
Usama Siddique
Keyword(s):  
Integral Operator ◽  
Integral Inequality ◽  
Fractional Integral ◽  
Fractional Integral Operator

In this paper the reverse fractional Minkowski integral inequality using extended Mittag-Leffler function with the corresponding fractional integral operator is proved, as well as several related Minkowskitype inequalities.

scholarly journals Riesz potential, Marcinkiewicz integral and their commutators on mixed Morrey spaces

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 931-944
Author(s):  
Andrea Scapellato
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Riesz Potential ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Higher Order ◽  
Lipschitz Class ◽  
Fractional Integral Operator ◽  
Marcinkiewicz Integral ◽  
Type Integral

This paper deals with the boundedness of integral operators and their commutators in the framework of mixed Morrey spaces. Precisely, we study the mixed boundedness of the commutator [b,I?], where I? denotes the fractional integral operator of order ? and b belongs to a suitable homogeneous Lipschitz class. Some results related to the higher order commutator [b,I?]k are also shown. Furthermore, we examine some boundedness properties of the Marcinkiewicz-type integral ?? and the commutator [b,??] when b belongs to the BMO class.

Chebyshev type inequality containing a fractional integral operator with a multi-index Mittag-Leffler function as a kernel

Analysis ◽  
2021 ◽  
Vol 41 (1) ◽  
pp. 61-67
Author(s):  
Kamlesh Jangid ◽  
S. D. Purohit ◽  
Kottakkaran Sooppy Nisar ◽  
Serkan Araci
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Multi Index ◽  
Type Integral ◽  
Special Case

Abstract In this paper, we derive certain Chebyshev type integral inequalities connected with a fractional integral operator in terms of the generalized Mittag-Leffler multi-index function as a kernel. Our key findings are general in nature and, as a special case, can give rise to integral inequalities of the Chebyshev form involving fractional integral operators present in the literature.

scholarly journals Refinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2059
Author(s):  
Hijaz Ahmad ◽  
Muhammad Tariq ◽  
Soubhagya Kumar Sahoo ◽  
Sameh Askar ◽  
Ahmed E. Abouelregal ◽  
...  
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Ostrowski Type Inequality ◽  
Special Cases ◽  
New Directions ◽  
Type Integral ◽  
Mathematical Sciences ◽  
Power Mean Inequality

In this article, first, we deduce an equality involving the Atangana–Baleanu (AB)-fractional integral operator. Next, employing this equality, we present some novel generalization of Ostrowski type inequality using the Hölder inequality, the power-mean inequality, Young’s inequality, and the Jensen integral inequality for the convexity of |Υ|. We also deduced some new special cases from the main results. There exists a solid connection between fractional operators and convexity because of their fascinating properties in the mathematical sciences. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. It is assumed that the results presented in this article will show new directions in the field of fractional calculus.

scholarly journals An extension of the multiple Erdélyi-Kober operator and representations of the generalized hypergeometric functions

2018 ◽  
Vol 21 (5) ◽  
pp. 1360-1376
Author(s):  
Dmitrii B. Karp ◽  
José L. López
Keyword(s):  
Integral Operator ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Generalized Hypergeometric Function ◽  
Generalized Hypergeometric Functions ◽  
Arbitrary Complex ◽  
Derivatives Of ◽  
Special Case

Abstract In this paper we investigate the extension of the multiple Erdélyi-Kober fractional integral operator of Kiryakova to arbitrary complex values of parameters by the way of regularization. The regularization involves derivatives of the function in question and the integration with respect to a kernel expressed in terms of special case of Meijer’s G-function. An action of the regularized multiple Erdélyi-Kober operator on some simple kernels leads to decomposition formulas for the generalized hypergeometric functions. In the ultimate section, we define an alternative regularization better suited for representing the Bessel type generalized hypergeometric function p−1Fp. A particular case of this regularization is then used to identify some new facts about the positivity and reality of zeros of this function.

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 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 Study of Incomplete Elliptic Integrals Pertaining to pΨq Function

2018 ◽  
Vol 14 (2) ◽  
pp. 11-18 ◽  
Author(s):  
Ravi Shanker Dubey ◽  
Anil Sharma ◽  
Monika Jain
Keyword(s):  
Fracture Mechanics ◽  
Integral Operator ◽  
Fractional Integral ◽  
Elliptic Integral ◽  
Elliptic Type ◽  
Liouville Type ◽  
Definite Integrals ◽  
Type Integral ◽  
Geometric Representations ◽  
Incomplete Elliptic Integrals

Abstract Elliptic-type integral plays a major role in the study of different problems of physics and technology including fracture mechanics. Many papers have been written for various families of elliptic-type integrals. Due to their applications here, we are presenting an organized study of certain generalized family of incomplete elliptic integral. The obtained results are basic in nature have various generalizations. While using the fractional integral operator of Riemann-Liouville type, we found several obvious hyper geometric representations. Which are further used to originate many definite integrals relating to their modules and amplitude of elliptic type generalized incomplete integrals.

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