Fractional Interval-valued Differential Equations And The Research Of Approximate Iteration By Upper And Lower Solutions

Fractional calculus theory as a generalized form of traditional calculus theory has attracted a wide range of scholars' attention. Since, it is not only a vital branch of theoretical subject of mathematics, but also is a main tool to study practical problems. In the last decades, the result concerning fuzzy functions theory also has triggered wide public concern. The intervalvalued functions analysis also become a hot issue, because it is an importance branch of fuzzy function theory. According to this circumstance, interval-valued analysis and interval-valued calculation have developed rapidly. In the meantime, the view appearances which combine the interval-valued analysis with the frictional calculus theory. In fact, it can better figure out computer engineering problems.Based on this reason, in this thesis, we will focus on the research of the concepts and properties of fractional interval-valued functions, fractional differential calculus equations and research of approximate concerning interval-valued functions etc. The thesis is organized as follows:In Chapter 1, we discuss the background, the domestic and foreign research situation of inter-valued functions, and elaborate the main work of this thesis.In Chapter 2, we will recall some significant definitions and conclusions regarding interval-valued functions and traditional fractional calculus. we present the basic notations on the fractional integral and differential calculus for interval-valued functions and then study the fractional integral and derivative for interval-valued functions.In Chapter 3, we prove, by using the inequality estimation and fixed point theorems in metric spaces,the existence of solutions for fractional interval-valued calculus equations.In Chapter 4, by constructing upper and lower solutions of fractional interval-valued differential equations, we obtain the solutions of fractional interval-valued differential equations via applying the method of monotone iteration.In Chapter 5, we sum up the main conclusions of the paper and presented our main work in the future.