250 citations · 878 across the 14 of their papers we have counts for
14 papers
A scaling law chaotic system
Xiao-Jun Yang
In this article, we propose an anomalous chaotic system of the scaling-law ordinary differential equations involving the Mandelbrot scaling law. This chaotic behavior shows the "Wu…
An insight on the fractal power law flow: from a Hausdorff vector calculus perspective
Xiao-Jun Yang
In the article we suggest the Hausdorff vector calculus based on the Chen Hausdorff calculus for the first time. The Gauss-Ostrogradsky-like, Stokes-like, and Green-like theorems,…
On all real zeros for a new class of the even entire function
Xiao-Jun Yang
In this article we propose a new class of the even entire function connected with the product and series with the real coefficients. We address a sufficient condition for all real…
A new class of the entire function of order one: a case study
Xiao-Jun Yang
In this article, a new class of the entire function of order one, expressed by the series and product representations with the real positive coefficients and complex zeros, is inve…
The scaling-law flows: An attempt at scaling-law vector calculus
Xiao-Jun Yang
In this paper, the scaling-law vector calculus, which is related to the connection between the vector calculus and the scaling law in fractal geometry, is addressed based on the Le…
On the Riemann-Hardy hypothesis for the Ramanujan zeta function
Xiao-Jun Yang
The Ramanujan zeta function was in proposed by an Indian mathematician Srinivasa Ramanujan. As an analogue of the Riemann hypothesis, an English mathematician Godfrey Harold…
A new fractional derivative involving the normalized sinc function without singular kernel
Xiao-Jun Yang, Feng Gao, J. A. Tenreiro Machado +1
In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution…
Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems
Xiao-Jun Yang
In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and va…
A new fractional operator of variable order: application in the description of anomalous diffusion
Xiao-Jun Yang, J. A. Tenreiro Machado
In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Lapl…
Some new applications for heat and fluid flows via fractional derivatives without singular kernel
Xiao-Jun Yang, Zhi-Zhen Zhang, H. M. Srivastava
This paper addresses the mathematical models for the heat-conduction equations and the Navier-Stokes equations via fractional derivatives without singular kernel.
A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow
Xiao-Jun Yang, H. M. Srivastava, J. A. Tenreiro Machado
In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytica…
A generalized model for Yang-Fourier transforms in fractal space
Xiao-Jun Yang
Local fractional calculus deals with everywhere continuous but nowhere differentiable functions in fractal space. The Yang-Fourier transform based on the local fractional calculus…
Expression of Generalized Newton Iteration Method via Generalized Local Fractional Taylor Series
Yang Xiao-Jun
Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from…
Generalized Local Fractional Taylor's Formula with Local Fractional Derivative
Xiao-Jun Yang
In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geo…