الفهرس 
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Abstract
The primary objective of this thesis is to outline the application of fractional calculus to some physical processes. Fractional calculus is used to modify existing models that use ordinary derivatives to new models using fractional derivatives. The new models exhibit more realistic results when compared with actual physical experiments. Fractional calculus is used to model the intermediate physical process between advection and dispersion. A new model to describe this intermediate process is introduced in finite and infinite domains. Adomian decomposition method is used to solve the model in the infinite case while a new numerical algorithm is introduced to approximate the solution in finite domains. The second part of the thesis is concerned with the introduction of a new fractional model that generalizes the Hodgkin and Huxley equations describing the action potential in neuron cells. The predictor corrector method is used to solve this fractional model.