On Ostrowski type inequalities

2016 ◽  
Vol 56 (1) ◽  
pp. 5-27 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Min-Jie Luo ◽  
R.K. Raina
Keyword(s):  
Hypergeometric Function ◽  
General Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Generalized Hypergeometric Function ◽  
Fractional Integral Operators ◽  
Special Cases

Abstract In this paper, new forms of Ostrowski type inequalities are established for a general class of fractional integral operators. The main results are used to derive Ostrowski type inequalities involving the familiar Riemann-Liouville fractional integral operators and other important integral operators. We further obtain similar types of inequalities for the integral operators whose kernels are the Fox-Wright generalized hypergeometric function. Several consequences and special cases of some of the results including applications to Stolarsky’s means are also pointed out.

scholarly journals Generalized Fractional Integral Operators andM-Series

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
A. M. Khan ◽  
R. K. Kumbhat ◽  
Amit Chouhan ◽  
Anita Alaria
Keyword(s):  
Hypergeometric Function ◽  
Numerical Computation ◽  
Power Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Generalized Hypergeometric Function ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

Two fractional integral operators associated with FoxH-function due to Saxena and Kumbhat are applied toM-series, which is an extension of both Mittag-Leffler function and generalized hypergeometric functionpFq. The Mellin and Whittaker transforms are obtained for these compositional operators withM-series. Further some interesting properties have been established including power function and Riemann-Liouville fractional integral operators. The results are expressed in terms ofH-function, which are in compact form suitable for numerical computation. Special cases of the results are also pointed out in the form of lemmas and corollaries.

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 Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 206 ◽  
Author(s):  
K.S. Nisar ◽  
D.L. Suthar ◽  
M. Bohra ◽  
S.D. Purohit
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Special Functions ◽  
Integral Operators ◽  
Factor X ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Mathieu Series ◽  
Srivastava’S Polynomials

Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral operators involving hypergeometric function in the kernel are applied to the product of Srivastava’s polynomials and the generalized Mathieu series, containing the factor x λ ( x k + c k ) − ρ in its argument. The results are expressed in terms of the generalized hypergeometric function and Hadamard product of the generalized Mathieu series. Corresponding special cases related to the Riemann–Liouville and Erdélyi–Kober fractional integral operators are also considered.

scholarly journals Pathway fractional integral operators of generalized k-wright function and k4-function

2017 ◽  
Vol 35 (2) ◽  
pp. 235 ◽  
Author(s):  
Dinesh Kumar ◽  
Ram Kishore Saxena ◽  
Jitendra Daiya
Keyword(s):  
Fractional Integral ◽  
Fractional Integration ◽  
Integral Operators ◽  
Wright Function ◽  
Finite Product ◽  
Fractional Integral Operators ◽  
Integral Formulas ◽  
Fractional Integration Operator ◽  
Composition Formula ◽  
Special Cases

In the present work we introduce a composition formula of the pathway fractional integration operator with finite product of generalized K-Wright function and K4-function. The obtained results are in terms of generalized Wright function.Certain special cases of the main results given here are also considered to correspond with some known and new (presumably) pathway fractional integral formulas.

scholarly journals On weighted inequalities for certain fractional integral operators

2006 ◽  
Vol 2006 ◽  
pp. 1-7
Author(s):  
R. K. Raina
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Gauss Hypergeometric Function ◽  
Weighted Inequalities ◽  
Fractional Integral Operators

This paper considers the modified fractional integral operators involving the Gauss hypergeometric function and obtains weighted inequalities for these operators. Multidimensional fractional integral operators involving the H-function are also introduced.

scholarly journals Some new inequalities for generalized convex functions pertaining generalized fractional integral operators and their applications

2021 ◽  
Vol 17 (1) ◽  
pp. 37-64
Author(s):  
A. Kashuri ◽  
M.A. Ali ◽  
M. Abbas ◽  
M. Toseef
Keyword(s):  
Differentiable Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Generalized Convex Functions ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators ◽  
New Inequalities

Abstract In this paper, authors establish a new identity for a differentiable function using generic integral operators. By applying it, some new integral inequalities of trapezium, Ostrowski and Simpson type are obtained. Moreover, several special cases have been studied in detail. Finally, many useful applications have been found.

Fractional operators in the matrix variate case

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
A. Mathai ◽  
Hans Haubold
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Natural Sciences ◽  
Gauss Hypergeometric Function ◽  
Fractional Operators ◽  
Fractional Integral Operators ◽  
The Matrix ◽  
Functional Forms ◽  
The Ideal

AbstractFractional integral operators connected with real-valued scalar functions of matrix argument are applied in various problems of mathematics, statistics and natural sciences. In this survey we start with considering the case of a Gauss hypergeometric function with the argument being a rectangular matrix. Subsequently, some fractional integral operators are introduced which complement theresults available on fractional operators in the matrix variate cases. Several properties and limiting forms are derived. Then the pathway idea is incorporated to move among several different functional forms. When these are used as models for problems in the natural sciences, then these can cover the ideal situations, neighborhoods, in between stages and paths leading to optimal situations.

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