Quasilinearization For Fractional Differential Equations

In this paper, the convergence of solutions to some fractional differential equations andsystem of fractional differential equations are studied, implying with quasilinearization method.The paper is composed of five chapters.In Chapter1, the subject of significance and research situation of the fractional differentialequations systems are introduced as well as the main work of the paper.In Chapter2, we employ the generalized quasilinearization method for initial value prob-lems of fractional differential equations, and constructs two monotone sequences, then proofsthey both converge uniformly and quadratically to the solution of the given problem.In Chapter3, we consider initial value problems of fractional functional differential equa-tions, and constructs two monotone sequences of upper and lower solutions. By using quasilin-earization technique, monotone sequences of approximate solutions that converge quadraticallyto a solution are obtained.In Chapter4, initial value problems of system of fractional differential equations with thedefinitions of upper and lower related solutions are discussed. By using generalized quasilin-earization method, two monotone sequences of iterates converging uniformly and quadraticallyto a solution of the problem are obtained.In Chapter5, a brief summary of this thesis and some advices about further developmentfor the theory of fractional differential equations are advanced.