in this paper, we present a fractional mathematical model of a one-dimensional phase phase change problem (stefan problem) with latent heat a power function of position. this model includes space-time fractional derivatives in caputo sense and time dependent surface heat flux. an approximate solution of this model is obtained by optimal homotopy asymptotic method (oham) to find an approximate s...

Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of fractional dynamic systems, this paper proposes a scale-dependent finite difference method (S-FDM) in which the non-uniform mesh depends on the time fractional deriva...

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...

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 present paper, two class of the general time-fractional Korteweg-de Vries equations (KdVs) are considered, a systematic investigation to derive Lie point symmetries of the equations are presented and compared. Each of them has been transformed into a nonlinear ordinary differential equation with a new independent variable are investigated. The derivative corresponding to time-fractional in t...

Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several suffic...

Evolution equations for anomalous diffusion employ fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. This paper develops the mathematical foundations of those operators.