In recent years increasing interests and considerable researches have been given to the fractional differential equations both in time and space variables. These are due to the applications of the fractional differential operators to problems in a wide areas of physics and engineering science and a rapid development of the corresponding theory. Motivating examples include the so-called continuo...

This paper presents a general solution for a space-and time-fractional diffusionwave equation defined in a bounded space domain. The space-and time-fractional derivatives are described in the Caputo sense. The application of Adomian decomposition method, developed for differential equations of integer order, is extended to derive a general solution of the space-and time-fractional diffusionwave...

We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time limit, is characterized by a universal power law. Contrasting this power law with the asymptotic FPT distribution from another type of anomalous diffusion exe...

We study, both analytically and by numerical modeling the equilibrium probability density function for an non-linear Lévy oscillator with the Lévy index α, 1 ≤ α ≤ 2, and the potential energy x 4. In particular, we show that the equilibrium PDF is bimodal and has power law asymptotics with the exponent −(α + 3). 1 Starting equations Recently, kinetic equations with fractional derivatives have a...

An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary conditions of Robin type. Finite element approximation in space is employed. To construct approximation in time, regularized twolevel schemes are used. The numeri...

Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...

Abstract. In earlier papers Saxena et al. (2002, 2003) derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which extended the work of Haubold and Mathai (2000). The object of the present paper is to investigate the solution of a unified form of fractional kinetic equation in which the free term contains any integrable function f(t),...

Mass transport such as movement of phosphorus in soils and solutes in rivers is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or super diffusion and is well described using a fractional adv...