الفهرس 
Chapter 1 IntroductionOnly 14 pages are availabe for public view
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Abstract
In this theses, chapter 1 provides a brief introduction and overview of the diffusion process. Its type and models that help in the description of the complex systems illustrate some kinds of diffusion. Chapter 2 deals with investigating the derivation and solution of the generalized fractional reaction advection-diffusion equation using Caputo time-derivative of the order γ and space fractional derivative of order α. We then illustrate a case where the system has a free source and found the final solution regarding the probability distribution function. Chapter 3 developed to describe the transportation of calmodulin-dependent protein kinase II (CaMKII) as a transportation model in the biological system; we suppose a new form of fractional reaction advection-diffusion equation that can describe this model. The diffusion of particles in biological cells and nerve cell as an important example is an extensive field of research at the interface between biology and physics. This thesis extends some central aspects in the theoretical description of such a transport process. They can be summarized in some issues. First, developing the fractional derivative equation of reaction- convection- diffusion equation and illustration is studied using a comb-like model as a toy model that is a good choice for describing diffusion in dendrites. Second, the equation is solved, and the results can explain the process of the transport of CAMII through the dendrite spin, which help in the transportation of information in the brain. We have derived and analyzed the fractional reaction convection diffusion equation with the Caputo time-derivative of the order γ and space fractional derivative of order α in a comb-like model random walker diffusive along the x-axis. The trapping processes may occur in the y-axis. The diffusion along x represents a fractal time process which exhibited an anomalous mean-squared displacement with initial Delta distribution .On the other hand, the diffusion along y-direction is given by mean-squared displacement . The main remark here is the direct connection between the fractional integral operators and the random disappearances or trapping along with the structure’s fingers. Also, we have introduced the co-moving technique in which the Laplace-Fourier technique can be applied to the resulting equation to give the solution in the form of Fox H-Function to get the solution. The studied model can describe some physical systems with trapping phenomena like diffusion in the dendritic spine of the nervous system as an example of biological systems in terms of H-function. We suggested a new solution to the CaMKII translocation wave, where activated CaMKII contaminant travels along dendrites with additional translocation inside spines. In conclusion, it should be observed that the above-mentioned physical arguments expound why anomalous transport of both CaMKII and neutral particles, namely subdiffusion, is feasible and help the application of the Comb model. These statements are based on dendritic spine geometry, which defines the expression for the transport expounded.