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...

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...

Absrtract. Group classification of systems of two coupled nonlinear reaction-diffusion equation with a general diffusion matrix started in papers [1], [2] is completed in present paper where all non-equivalent equations with triangular diffusion matrix are classified. In addition, symmetries of diffusion systems with nilpotent diffusion matrix and additional first order derivative terms are des...

Fractional differential equations have become a fundamental modelling approach for understanding and simulating the many aspects of non-locality spatial heterogeneity complex materials systems. Yet, while real-order fractional operators are nowadays widely adopted, little progress has been made in extending such to complex-order counterparts. In this work, we introduce new definitions Laplacian...

Transport phenomena involved in the leaching of a radioactive material from a composite matrix into surrounding water are investigated using three methods based on theoretical equations. These are: diffusion equation derived for a plane source model, rate equation for diffusion coupled with a first-order reaction and an empirical method employing a polynomial equation. The obtained results are ...

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...

This paper is concerned with the existence, uniqueness and globally asymptotic stability of traveling wave fronts in the quasi-monotone reaction advection diffusion equations with nonlocal delay. Under bistable assumption, we construct various pairs of superand subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing trav...