Project supported by the National Natural Science Foundation of China(Grant No.11772032);the Science Foundation of North University of China(Grant No.11026829).
The turbulence governed by the Navier-Stokes equation is paramount in many physical processes.However,it has been considered as a challenging problem due to its inherent nonlinearity,non-equilibrium,and complexity.Her...
the Deanship of Scientific Research at King Khalid University for funding their work through Research Group Program under grant number(G.P.1/160/40)。
We deal with the Wick-type stochastic fractional Korteweg de–Vries(KdV) equation with conformable derivatives.With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set...
Project supported by the National Natural Science Foundation of China(Grant No.11471262);Henan University of Technology High-level Talents Fund,China(Grant No.2018BS039)
The fractional Feynman-Kac equations describe the distributions of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, wher...
In this paper, we introduce and propose exact and explicit analytical solutions to a novel model of the nonlinear Schr¨odinger(NLS) equation. This model is derived as the equation governing the dynamics of modulated ...
Project supported by the National Natural Science Foundation of China(Grant No.61271395);the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20161513)
Because of the fractional order derivatives, the identification of the fractional order system(FOS) is more complex than that of an integral order system(IOS). In order to avoid high time consumption in the system...
In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equa- tion are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For thi...
supported by the National Natural Science Foundation of China(Grant No.61174193);the Doctorate Foundation of Northwestern Polytechnical University,China(Grant No.CX201409)
This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discretetime system with linear system state equation. The first paper established a derivative unscented Kal...
Project supported by the Higher Education Commission of Pakistan
This paper presents an adaptive step-size modified fractional least mean square (AMFLMS) algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptati...
Project supported by the Higher Education Commission of Pakistan
A method of modifying the architecture of fractional least mean square (FLMS) algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adap...
Project supported by the National Natural Science Foundation of China(Grant No.10671156);the Natural Science Foundation of Shaanxi Province of China(Grant No.SJ08A05)
By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = (A(u)Ux)x + eB(u, Ux). A complete classification of t...