In this paper, a numerical efficient method is proposed for the solution of time fractional mobile/immobile equation. The fractional derivative of equation is described in the Caputo sense. The proposed method is based on a finite difference scheme in time and Legendre spectral method in space. In this approach the time fractional derivative of mentioned equation is approximated by a scheme of ord...

In this work, an initial value problem is discussed for a fractional differential equation of variable-order. By means of some analysis techniques and Arzela-Ascoli theorem, existence result of solution is obtained; Using the upper solutions and lower solutions and monotone iterative method, uniqueness existence results of solutions are obtained.

The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fractional generaliz...

The standard diffusion processes are known to be obtained as the limits of appropriate random walks. These prelimiting walks can quite different, however. coefficient made responsible for size jumps or intensity jumps. limit does not feel difference. situation changes if we model jump-type approximations via CTRW with non-exponential waiting times. If make and take times from domain attraction ...

Several approaches to the formulation of a fractional theory calculus "variable order" have appeared in literature over years. Unfortunately, most these proposals lack rigorous mathematical framework. We consider an alternative view on problem, originally proposed by G. Scarpi early seventies, based naive modification representation Laplace domain standard kernels functions involved (constant-o...