Research On The Existence Of Solutions And Topological Structure Of Solution Set For Two Classes Of Differential Inclusions

Differential inclusion is a generalized form of differential equations.Some complex natural phenomena can be modeled by differential inclusion models,such as typhoon transit model,population model,and artificial neural network model.In order to improve the research on the theory of differential inclusions,this article discusses the existence of solutions for sequential fractional hybrid differential inclusions with Hadamard derivative,and the existence of solutions and the topological structure of solution sets for neutral semilinear measures evolution inclusions.The specific distribution of the article is as follows:Chapter 1,the research background and development status of differential inclusion theory(including fractional differential inclusion,measure differential inclusion,etc.)are described.Chapter 2,fractional calculus theory,set-valued analysis theory,noncompact measure theory and other basic theories are introduced.Chapter 3,by using the Dhage fixed point theorem of multivalued mapping and CovitzNadler fixed point theorem,the existence of two classes of mild solutions for Hadamard sequential fractional hybrid differential inclusion with hybrid integral boundary conditions is obtained.At the end of this chapter,two examples are given to verify the effectiveness of the results,and the main research contents of this chapter are summarized.Chapter 4,firstly,by using Górniewicz-Lassonde fixed point theorem,the existence of solutions and the compactness of solution sets of neutral semilinear measure evolution inclusions under weak conditions are obtained.Secondly,under the above conditions,by combining the equivalence of R?-structure,Hyman theorem,and by constructing a continuous function that can make the solution set homotopy at a single point,the contractibility of the solution set is explained,and then the R?-structure of the solution set of this kind of differential inclusion is obtained.At the end of this chapter,the main research contents of this chapter are summarized.Chapter 5,the article is summarized and the future work is prospected.