In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar to the reaction-diffusion master equation (RDME) description when those SPDEs are spatially discretized and reactions are modeled as a source term having Poi...

We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be lack of accuracy if the POD basis depending on a set of parameters is used to approximate the problem depending on a different set of parameters. We are intere...

The objective of this article is to carry out an approximate analytical solution of the time fractional order Cauchy-reaction diffusion equation by using a semi analytical method referred as the fractional-order reduced differential transform method (FRDTM). The fractional derivative is illustrated in the Caputo sense. The FRDTM is very efficient and effective powerful mathematical tool for sol...

This paper addresses the stability problem of genetic regulatory networks by involving spatial diffusion concentration, discrete and infinite distributed delays. By using theories partial differential equation Lyapunov stability, global exponential criteria in algebraic form are derived for reaction (RDGRNs) with The conditions simple can be directly calculated parameters networks. Moreover, th...

This paper concerns with the balancing theory for the system governed by diffusion partial differential equation, which is refereed here as infinite dimensional system or distributed-parameter system. Based on the eigenvalue-eigenfunction structure of Laplacian differential operator, the approximate controllability and initial observability are constructed. In order to perform the balanced real...

The distribution of the roots of a second order transcendental polynomial is analyzed, and it is used for solving the purely imaginary eigenvalue of a transcendental characteristic equation with two transcendental terms. The results are applied to the stability and associated Hopf bifurcation of a constant equilibrium of a general reaction–diffusion system or a system of ordinary differential e...

In this article we study the convergence and the error bound for the solution of the convection diffusion reaction equation using overlapping Schwarz wave form relaxation method combined with the first order fractional splitting method (Strang’s splitting) as basic solver. We extended the study to solve decoupled and coupled system of equations of same class in order to demonstrate the effect o...