Numerical Solution of Fractional Order Differential Equations Using Wavelets Methods

         The main theme of this thesis is oriented about three objects:
 The first one is to study the fundamental concepts of fractional calculus which are needed for finding the numerical solution of the differential equations (ordinary and partial) of fractional order. The second objective is about finding the numerical solution of the non-linear ordinary differential equations of fractional order using wavelets methods which are Haar wavelets method, Chebyshev wavelets method and Legendre wavelets method. The main idea of these methods is to reduce the ordinary differential equation of fractional order into a system of algebraic equations then solved the obtained system. The
solution of this system will give us the values of the coefficients of the desired solution which is expressed in an infinite series thus greatly simplifying such equations.