| In this paper, based on the literature of [31] about basic knowledge of learning,and inspired by the literature [3] and [7], I determine the study of the party: A class of fractional order differential equations with multi-point boundary conditions, a class of singular fractional order differential equations. The existence of solutions of differential equations in literature [11]-[15] is studied, and the research on the positive solutions of the equations is studied by [16]-[18]. The existence of positive solutions for two kinds of equations under different conditions is studied. Based on literature [3] and [19]-[21]about the singularity of the equations, the singularity is processed by the condition（H1） in this paper, and the study of the singular fractional differential equation is established. Based on the research of the equation of the multi-point boundary condition of [22]-[27], this paper solves the Green’s function. The existence of positive solutions of the equations is studied by using the properties of Green’s function. Based on different research methods of the other side in [28]-[32], this paper determines the existence of the solution by using the fixed point theorem of cone tension compression.According to the content, this paper can be divided into the following three chapters:In the first chapter, we collect some basic concepts, definitions and basic theorems that we use in this paper.In the second chapter, the fractional order differential equation with multi-point boundary conditions is studied, which meets the conditions, （a1） αi> 0, 1 ≤ i ≤ n, 1 < η1< η2< · · · < ηn< 1 and （a2） h（t） ∈ L[0, 1], and h（t） is not identically zero in any subinterval of（0, 1）, h（t） is a nonnegative function,（a3） f : [0, 1] × [0, ∞) × R â†' [0, ∞) is continuous.In the third chapter, the existence of positive solutions of singular fractional differential equations is studied, which meets the condition,（H1）f:C[（0,1）×R+,R+],且f（t,u）≤h1（t）h2（u）,t∈（0,1）,u∈R+,h1∈C[（0,1）,R+],h2∈C[R+,R+]. |
PDF Full Text Request