Some new local fractional integral inequalities

2017 ◽  
Vol 10 (2) ◽  
pp. 133-143
Author(s):  
Mehmet Zeki Sarikaya ◽  
Hüseyin Budak
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Local Fractional Integral

scholarly journals A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Wei Wei ◽  
H. M. Srivastava ◽  
Yunyi Zhang ◽  
Lei Wang ◽  
Peiyi Shen ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Local Fractional Integral ◽  
Fractal Space ◽  
Integral Analogue

Anderson's inequality (Anderson, 1958) as well as its improved version given by Fink (2003) is known to provide interesting examples of integral inequalities. In this paper, we establish local fractional integral analogue of Anderson's inequality on fractal space under some suitable conditions. Moreover, we also show that the local fractional integral inequality on fractal space, which we have proved in this paper, is a new generalization of the classical Anderson's inequality.

SOME LOCAL FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED PREINVEX FUNCTIONS AND APPLICATIONS TO NUMERICAL QUADRATURE

Fractals ◽  
2019 ◽  
Vol 27 (05) ◽  
pp. 1950071 ◽  
Author(s):  
WENBING SUN
Keyword(s):  
Numerical Integration ◽  
Error Estimates ◽  
Fractional Integral ◽  
Numerical Quadrature ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Parallel Development ◽  
Special Values ◽  
Local Fractional Integral ◽  
Preinvex Functions

In this paper, a new identity with parameters involving local fractional integrals is derived. Using this identity, some general local fractional integral inequalities for generalized preinvex functions are established. A parallel development is deduced for generalized preconcave functions. Taking special values for the parameters, some generalized midpoint inequalities, trapezoidal inequalities and Simpson inequalities are obtained. Finally, as some applications, error estimates of numerical integration for local fractional integrals are given.

THE STRUCTURAL FEATURES OF HILBERT-TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITIES WITH ABSTRACT HOMOGENEOUS KERNEL AND ITS APPLICATIONS

Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050111
Author(s):  
YINGDI LIU ◽  
QIONG LIU
Keyword(s):  
Fractional Integral ◽  
Structural Characteristics ◽  
Sufficient Conditions ◽  
Constant Factor ◽  
Integral Inequalities ◽  
Homogeneous Kernel ◽  
Best Constant ◽  
Local Fractional Integral ◽  
Best Constant Factor ◽  
Hilbert Type

In this paper, by using the theory of local fractional calculus and some techniques of real analysis, the structural characteristics of Hilbert-type local fractional integral inequalities with abstract homogeneous kernel are studied. At the same time, the necessary and sufficient conditions for these inequalities to take the best constant factor are discussed. As an application, some best constant factor inequalities with specific kernels are obtained.

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 Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Samaira Naz ◽  
Muhammad Nawaz Naeem ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Derivative Operator ◽  
Practical Applications ◽  
Mathematical Problems ◽  
Grüss Type Inequalities

AbstractIn this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions. For these functions, we develop some new fractional integral inequalities. Our results with this new derivative operator are capable of evaluating several mathematical problems relevant to practical applications.

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.

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