Research On The Existence Of Solutions For Several Boundary Value Problem Of Fractional Differential Inclusions

This thesis mainly investigates the existence of solutions of multipoint and integral boundary value problems of Caputo type fractional differential inclusions. It is composed of five chapters.In first chapter, we introduce the historical background and the recent development of the fractional differential inclusion. Also, the main results are briefly introduced.In second chapter introduces some preliminary related to this thesis, in-cluding some definitions and lemmas.In three chapter, we discuss the existence of solutions of multipoint boundary value problems of Caputo type fractional differential inclusions under the conditions of convex and nonconvex valued maps. In the convex case, non-linear alternative for Kakutani maps was first used to establish the sufficient condition under which the multi-point boundary value problem of factional differential inclusion had at least one positive solution. Then, by cone contrac-tion mapping fixed point theorem, another sufficient condition under which the boundary value problem has at least two positive solutions was established. In the nonconvex case, by means of Bressan-Colombo continuous selection theo-rem and Schauder fixed point theorem, the sufficient conditions under which the boundary value problem has at least one solution was established. Then, with contraction mapping theorem, the sufficient condition under which the boundary value problem has at least one solution was established.In four chapter, we explored the existence of solutions of integral bound-ary value problems of Caputo type fractional differential inclusions under the conditions of convex and nonconvex valued maps. Similarly, nonlinear alter-native for Kakutani maps, Bressan-Colombo continuous selection theorem, fixed point theorem and contraction mapping theorem are used to establish the sufficient condition guaranteeing the existence of solutions. In the convex case, by virtue of fixed point theorem, some criteria of the existence of at least three solutions of boundary value problems are yielded.In last chapter, we propose some plans for the research to be done in the future.The results of this thesis improve and generalize the known results in the literature.