The Numerical Solution of Linear Variable Order Fractional Differential Equations Using Bernstein Polynomials

 The main theme of this thesis is oriented about three objects:
The first objective is to study the basic concepts of fractional calculus and variable-order fractional differential equations.The second objective is about solving numerically the variable-order fractional differential equations using operational matrices of Bernstein polynomials.The proposed approach will transform the variable-order fractional differential equations into the product of some matrices which can be considered as a linear system of algebraic equations, after solving the resulting system the numerical solution can be obtained. The third objective is to find the numerical solution of multiterm variable-order fractional differential equations using operational matrices of Bernstein polynomials, also the proposed method will transform the multiterm variable-order fractional differential equations into the product of matrices in other words into a system of linear algebraic equations, and the numerical solution will be reached after solving the resulting system.