Methods for solving fractional differential equations

Abstract

Bu ¸calısmada Kesirli Mertebeden Diferansiyel Denklemlerin analitik ve sayısal ¸cozumy¨ontemleri arastırılmıstır. Bu metodlar Grenn's Fonksiyonu Metodu, AdomianDecomposition Metodu, Kuvvet Serisi Metodu ve Sonlu Fark S¸emaları Metodlarıdır.Cozum yontemleri Bagley-Torvik diye bilinenAD2t x (t) + BD3=2t x (t) + Cg (x) = f (t) ;A 6= 0 ve B;C 2 R ¨ozel bir kesirli mertebeden diferansiyel denklem ile orneklendirilmistir.Sonu¸clar sayısal ve grafiksel olarak karsılastırılıp, bilgisayar programları vealgoritmaları yazılıp uygulanmıstır.

In this study, methods for analytical and numerical solutions of the Fractional DifferentialEquations are investigated. These methods are Green?s Function Method,Adomian Decomposition Method, Power Series Method and Finite Difference Method.Also, they are illustrated with a special type of fractional differential equationAD2t x (t) + BD3=2t x (t) + Cg (x) = f (t) ;where A 6= 0 and B;C 2 R which is known as Bagley-Torvik equation. The resultsare compared both numerically and graphically, computer programmes andalgorithms are presented.Keywords: Fractional differential equations, Bagley-Torvik equation, Green?sFunction method, power series method, ADM, FDM.