scholarly journals New Newton's Type Estimates Pertaining to Local Fractional Integral via Generalized p-Convexity with Applications

Fractals ◽  
2021 ◽  
Author(s):  
Yong-Min Li ◽  
Saima Rashid ◽  
Zakia Hammouch ◽  
Dumitru Baleanu ◽  
Yu-Ming Chu
Keyword(s):  
Fractional Integral ◽  
Local Fractional Integral

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.

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

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 Existence of local fractional integral equation via a measure of non-compactness with monotone property on Banach spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Rabha W. Ibrahim ◽  
Ravi P. Agarwal ◽  
N. H. Can
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Partially Ordered ◽  
Fractional Integral Equation ◽  
Local Fractional Integral ◽  
Ordered Banach Spaces

AbstractIn this paper, we discuss fixed point theorems for a new χ-set contraction condition in partially ordered Banach spaces, whose positive cone $\mathbb{K}$ K is normal, and then proceed to prove some coupled fixed point theorems in partially ordered Banach spaces. We relax the conditions of a proper domain of an underlying operator for partially ordered Banach spaces. Furthermore, we discuss an application to the existence of a local fractional integral equation.

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.

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