الفهرس 
Some Mathematical ToolsOnly 14 pages are availabe for public view
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Abstract
Abstract
This thesis is a contribution on numerical studies for some mathemat- ical models in Biology. We generalized two different models for describing Salmonella epidemic. The first model is the fractional order Salmonella trans- mission model-I and the second one is the fractional order delayed Salmonella transmission model-II. Some analytical studies of the properties of the intro- duced systems were run out and the stability of equilibrium points is studied. The numerical methods which were used in this thesis are non standard finite difference methods and the weighted average finite difference method. Theo- rems with their proofs are presented to study the stability analysis and some properties of the proposed finite difference schemes. The concept of the frac- tional derivative in this thesis is considered in the sense of Caputo fractional derivative for the time derivative. Numerical test examples for the proposed models are presented to show the accuracy, applicability, and efficiency of the proposed techniques for solving biological stiff systems.
Keywords: Salmonella epidemic; Nonstandard finite difference; Fractional cal- culus; Caputo fractional derivative; Weighted average finite difference method; Stability analysis.