Differential equations of fractional order and a study on numerical solutions

In this thesis which are; primarily required definitions and theorems are given in the studies intended for the mathematical application of fractional differentiation and fractional integration concepts. Riemann - Liouville integral and differential operators and Caputo differential operator are introduced; some general characteristics of them and relations among them are mentioned. Existence and uniqueness of solutions of initial value problems involving fractional order differential equations under certain conditions are considered by the help of fixed point theorems. Dependence on parameters of initial value problems involving fractional order differential equation, namely how the solution is effected in the case of perturbation of parameters is investigated. As a numerical method, Adam's type predictor - corrector method is investigated for the initial value problems involving fractional order differential equation, error analysis of this method is mentioned and lastly an application for this method has been added. Results are expressed on the tables. This method is observed as a method that quickly operating, easily being set up of algorithms, giving good and reliable, high sensitive results.