Solutions for the systems of fractional order ordinary differential equations using the adomian decomposition method and the variational iteration method

In this thesis study, solutions of systems of fractional order differential equations by the Variational Iteration Method and the Adomian Decomposition Method are studied. The fractional order SIR (Susceptible-Infected-Recovered) model is considered as an application. The thesis study consists of five main sections. In the introduction section, a literature review of the fractional order differential equations, solution of fractional order differential equations by the Variational Iteration Method and the Adomian Decomposition Method, and fractional order SIR models is given. In the first section, the definitions of some basic functions, the fractional derivatives, and the fractional integrals are presented. In the second section, the solutions of the fractional order differential equations system by the Variational Iteration Method and the Adomian Decomposition Method are given. The third section is devoted to the application of these methods to a basic SIR model. The fourth section presents numerical results obtained by the Variational Iteration Method and the Adomian Decomposition Method in graphical and tabular forms. Moreover, the obtained numerical results are compared, and the accuracy of the results has been seen. Finally, the last section is the result section.