An Efficient Algorithm Based On Fractional Legendre-Collocation Method for Solving Fractional Initial Value Problems

Ahmed Salameh Hussein Abu Omer

Abstract

In recent years, fractional calculus (the branch of calculus that generalizes the derivative of a function to non-integer order) has been a subject of numerous investigations by scientists from mathematics, physics and engineering communities. The interest in this area of research arises mainly from its applications to many models in the fields of fluid mechanics, electromagnetic, acoustics, chemistry, biology, physics and material sciences. In this thesis, we present a numerical algorithm for solving linear and non-linear fractional initial value problems. This numerical algorithm is based on the spectral method with fractional Legendre functions as basis. Then the collocation method is implemented to turn the original fractional initial value problem into algebraic system. Several examples are discussed to illustrate the efficiency and accuracy of the present scheme.