An Improvement of Local Fractional Integral Minkowski’s Inequality on Fractal Space

2014 ◽  
Vol 998-999 ◽  
pp. 980-983
Author(s):  
Guang Sheng Chen
Keyword(s):  
Fractional Integral ◽  
Minkowski’S Inequality ◽  
Local Fractional Integral ◽  
Fractal Space

In the paper, we establish some improvements of Minkowski’s inequality on fractal space via the local fractional integral.

Applications of Yang-Fourier Transform to Local Fractional Equations with Local Fractional Derivative and Local Fractional Integral

2012 ◽  
Vol 461 ◽  
pp. 306-310 ◽  
Author(s):  
Wei Ping Zhong ◽  
Feng Gao ◽  
Xiao Ming Shen
Keyword(s):  
Fourier Transform ◽  
Fractional Derivative ◽  
Fractional Integral ◽  
Fractional Fourier Transform ◽  
Local Fractional Derivative ◽  
Fractional Equations ◽  
Local Fractional Integral ◽  
Fractal Space

Yang-Fourier transform is the generalization of the fractional Fourier transform of non-differential functions on fractal space. In this paper, we show applications of Yang-Fourier transform to local fractional equations with local fractional derivative and local fractional integral

scholarly journals Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Saad Ihsan Butt ◽  
Praveen Agarwal ◽  
Saba Yousaf ◽  
Juan L. G. Guirao
Keyword(s):  
Probability Density Function ◽  
Convex Function ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integrals ◽  
Fractal Sets ◽  
Local Fractional Integral ◽  
Fractal Space ◽  
Harmonic Convex ◽  
Harmonically Convex Function

AbstractIn this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.

A Subdividing of Local Fractional Integral Holder’s Inequality on Fractal Space

2014 ◽  
Vol 998-999 ◽  
pp. 976-979
Author(s):  
Guang Sheng Chen
Keyword(s):  
Fractional Integral ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Local Fractional Integral ◽  
Fractal Space

In this paper, we establish a subdividing of Hölder’s inequality via local fractional integral. Its reverse version is also given.

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.

scholarly journals Some Further Generalizations of Hölder's Inequality and Related Results on Fractal Space

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Guang-Sheng Chen ◽  
H. M. Srivastava ◽  
Pin Wang ◽  
Wei Wei
Keyword(s):  
Fractional Integral ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Special Cases ◽  
Local Fractional Integral ◽  
Fractal Space

We establish some new generalizations and refinements of the local fractional integral Hölder’s inequality and some related results on fractal space. We also show that many existing inequalities related to the local fractional integral Hölder’s inequality are special cases of the main inequalities which are presented here.

scholarly journals Hermite-Hadamard type inequalities for generalized convex functions on fractal sets style

2018 ◽  
Vol 38 (1) ◽  
pp. 101-116 ◽  
Author(s):  
Muharrem Tomar ◽  
Praveen Agarwal ◽  
Junesang Choi
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Generalized Convex Functions ◽  
Fractal Sets ◽  
Special Cases ◽  
Logarithmic Means ◽  
Local Fractional Integral ◽  
Generalized Arithmetic

We aim to  establish certain generalized Hermite-Hadamard's inequalities for generalized convex functions via local fractional integral. As special cases of some of the results presented here, certain interesting inequalities involving generalized arithmetic and logarithmic means are obtained.

scholarly journals A New Neumann Series Method for Solving a Family of Local Fractional Fredholm and Volterra Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-Jing Ma ◽  
H. M. Srivastava ◽  
Dumitru Baleanu ◽  
Xiao-Jun Yang
Keyword(s):  
Integral Operator ◽  
Integral Equations ◽  
Fractional Integral ◽  
Neumann Series ◽  
Volterra Integral Equations ◽  
Fractional Integral Operator ◽  
Series Method ◽  
Operator Type ◽  
Local Fractional Integral

We propose a new Neumann series method to solve a family of local fractional Fredholm and Volterra integral equations. The integral operator, which is used in our investigation, is of the local fractional integral operator type. Two illustrative examples show the accuracy and the reliability of the obtained results.

A (⋆, ∗)-Based Minkowski’s Inequality for Sugeno Fractional Integral of Order α > 0

2015 ◽  
Vol 18 (4) ◽  
Author(s):  
Azizollah Babakhani ◽  
Hamzeh Agahi ◽  
Radko Mesiar
Keyword(s):  
Fractional Integral ◽  
Fuzzy Measure ◽  
Minkowski’S Inequality ◽  
Fuzzy Integral ◽  
Binary Operations

AbstractWe first introduce the concept of Sugeno fractional integral based on the concept of g-seminorm. Then Minkowski’s inequality for Sugeno fractional integral of the order α > 0 based on two binary operations ⋆, ∗ is given. Our results significantly generalize the previous results in this field of fuzzy measure and fuzzy integral. Some examples are given to illustrate the results.

Local Fractional Fourier Series With Applications to Representations of Fractal Signals

2013 ◽  
Author(s):  
Dumitru Baleanu ◽  
Xiao-Jun Yang
Keyword(s):  
Fourier Series ◽  
Integral Operator ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Series Representations ◽  
Local Fractional Integral ◽  
Fractal Signal

In this paper we discuss the local fractional Fourier series representations of fractal signals. Fractal signal processes are described within the local fractional integral operator. Four examples are presented in order to illustrate the developed technique.

scholarly journals New model for local fractional integral of Chebyshev polynomials for image denoising

2019 ◽  
pp. 22-28
Author(s):  
Suzan J Obaiys ◽  
Hamid A Jalab ◽  
Rabha W Ibrahim
Keyword(s):  
Image Denoising ◽  
Chebyshev Polynomials ◽  
Fractional Integral ◽  
Signal To Noise Ratio ◽  
Similarity Index ◽  
Structural Similarity ◽  
Input Image ◽  
Convolution Product ◽  
Local Fractional Integral ◽  
Image Pixels

The use of local fractional calculus has increased in different applications of image processing. This study proposes a new algorithm for image denoising to remove Gaussian noise in digital images. The proposed algorithm is based on local fractional integral of Chebyshev polynomials. The proposed structures of the local fractional windows are obtained by four masks created for x and y directions. On four directions, a convolution product of the input image pixels with the local fractional mask window has been performed. The visual perception and peak signal-to-noise ratio (PSNR) with the structural similarity index (SSIM) are used as image quality measurements. The experiments proved that the accomplished filtering results are better than the Gaussian filter. Keywords: local fractional; Chebyshev polynomials; Image denoising

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