Weighted Residual Methods for Linear Fractional Differential Equations

In Chapter one, an introduction of the fractional calculus is presented. In Chapter two: gives the definition of expansion method and weighted residual methods. Also important theories and definitions concerning the converge and stability of methods for solving a system of equations are given in this chapter. In Chapter three Both fractional Fredholm integro-differential equations (FFIDE) and fractional Volterra integro-differential equations (FVIDE) will be solved using the weighted residual methods with the orthogonal functions as a basis functions to approximate the unknown function within the proposed methods. Several examples are included. In Chapter four Both FFIDE and FVIDE will be solved using the weighted residual methods with the spline functions as a basis functions to approximate the unknown function within the proposed methods. Several examples are included. Chapter five includes conclusions and recommendations for future work and comparisons with the methods are given in tables.