It may often be tempting to take a fractional diffusion equation and simply create a fractional reactiondiffusion equation by including an additional reaction term of the same form as one would include for a standard Fickian system. However, in real systems, fractional diffusion equations typically arise due to complexity and heterogeneity at some unresolved scales. Thus, while transport of a c...

in this work, we apply the radial basis functions for solving the time fractional diffusion-wave equation defined by caputo sense for                         . the problem is discretized in the time direction based on finite difference scheme and is continuously approximated by using the radial basis functions in the space direction which achieves the semi-discrete solution. numerical results s...

The fuzzy fractional differential equation explains more complex real-world phenomena than the does. Therefore, numerous techniques have been timely derived to solve various time-dependent models. In this paper, we develop two compact finite difference schemes and employ resulting obtain a certain solution for time-fractional convection–diffusion equation. Then, by making use of Caputo derivati...

In this paper, we consider the numerical solution of the time fractional diffusion equation. Essentially, the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term. In the former case, the first-order time derivative is replaced by a fractional derivative, making the problem global in time. We propose a spectral method in both temporal and s...

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two mai...

The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin-Barnes integral representation. Such solution is proved to be related via a Laplace-type integral to the Fox-Wright functions. A series expansion is also provided in order to point out the distribution of time-scales r...

Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary In the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann...