الفهرس 
CHAPTER IOnly 14 pages are availabe for public view
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Abstract
Fractional differential equations (FDEs) appear more and more frequently in various research areas and engineering applications including fluid flow, electrical networks, control theory, electromagnetic theory, optics, potential theory, biology, chemistry, probability, statistics, diffusion theory, fractals theory, electrochemistry, viscoelasticity, and biological systems.
In this work, we generalized some of bio-mathematical models by using partial differential equations of fractional order, and we found analytical solutions for these models by using generalized differential transform method (GDTM) and Adomian’s decomposition method (ADM).
This thesis contains sex chapters, which are briefly described as follow:
Chapter I
Contain the basics of differential and integral equations with fractional orders.
Chapter II
Solutions were found for a three generalized biological models:
1. Generalized Fisher equation
2. Generalized Fitzhugh–Nagumo equation
3. Generalized Biological Population Model
Chapter III
Solutions were found for generalized reaction-diffusion model for bacteria growth called (Bacillus subtilis) which describe the evolution of bacteria pattern formation:
1. Generalized reaction-diffusion model of fractional-order for bacterial growth (in one dimension)
2. Generalized reaction-diffusion model of fractional-order for bacterial growth (in two dimensions).
Chapter IV
Solutions were found for generalized reaction-diffusion model for bacteria growth with chemotaxis called (Escherichia coli (E. coli)):
1. Generalized reaction-diffusion-chemotaxis model of fractional-orders for bacterial growth (in one dimension).
2. Generalized reaction-diffusion-chemotaxis model of fractional-order for bacterial growth (in two dimensions).
Chapter V
Solutions were found for generalized reaction-diffusion model for bacteria growth with chemotaxis called (Escherichia coli (E. coli)) in a semi-solid medium and in a liquid medium:
1. Generalized reaction-diffusion bacterial chemotaxis model in a semi-solid medium.
2. Generalized reaction-diffusion bacterial chemotaxis model in a liquid medium
Chapter VI
Solutions were found for generalized reaction-diffusion model for bacteria growth with chemotaxis called (Escherichia coli (E. coli)) in a diffusion gradient chamber:
1. Generalized reaction-diffusion bacterial chemotaxis in a diffusion gradient chamber