With the rapid development of the Yangtze River economic belt, the amount of waste-sewage water discharged into the Yangtze River basin increases sharply year by year, which has impeded the sustainable development of the Yangtze River basin. The water security along the Yangtze River basin is very important for China, It is something aboutwater security of roughly one-third of China's populatio...

The power law wave equation uses two different fractional derivative terms to model wave propagation with power law attenuation. This equation averages complex nonlinear dynamics into a convenient, tractable form with an explicit analytical solution. This paper develops a random walk model to explain the appearance and meaning of the fractional derivative terms in that equation, and discusses a...

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

Based on the Riemannand Caputo definition of the fractional derivative we use the fractional extensions of the standard rotation group SO(3) to construct a higher dimensional representation of a fractional rotation group with mixed derivative types. An extended symmetric rotor model is derived, which predicts the sequence of magic proton and neutron numbers accurately. The ground state properti...

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given...

This paper is devoted to the study of the flatness property of linear time-invariant differential systems of fractional systems. We give two characterizations of fractionally flat outputs and algorithms to compute them. We then present an application to a two dimensional thermal system that we approximate by a fractional model of order 1 2 , that is fractionally flat. Trajectory planning of the...

This paper presents a methodology to determine all-digital phase-locked loop (ADPLL) circuit variables based on required design specifications, including output phase noise, fractional spur and locking time. An analytical model is developed to characterize the effects of different noise sources on ADPLL output phase noise and fractional spur. Applying the proposed noise model, circuit variables...

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...

In this paper, a fractional-order model for the spread of computer viruses with saturated treatment rate is presented. This model consists of three components: Susceptible, Infectious, and Recovered. The SIR epidemic model with saturated treatment rate is considered. The stability of the disease free and endemic equilibrium points are studied. The global stability of the disease free equilibriu...