Research On Solutions Of Boundary Value Problems For Caputo-Hadamard Type Fractional Differential Equations

Fractional calculus is one of the hot issues that many scholars have paid at-tention to in recent years,and it has achieved rapid development in the boundary value problem of fractional differential equations.Many natural phenomena can be presented by it and there are some areas that need further expansion and improve-ment.In chapter 2 of this paper,we consider the following two-point boundary value problem for fractional differential equation(?)Where 1<?<2,?>0,f:[1,e]×R?R is a given continuous function,CH D? is the Caputo-Hadamard fractional derivative.Based on the the method of upper and lower solutions and fixed point theorem,the existence and uniqueness of solutions are obtained.In chapter 3,we discuss the multi-point boundary value problems for Caputo-Hadamard type fractional differential equation(?)Where 2<??3,CHD? is the Caputo-Hadamard fractional derivative.f:[1,e]×R?R is a given continuous function,we converse from differential equations into integral equations of the Green function.The uniqueness of solution is established by Banach contraction principle,whereas the existence of solutions is derived from Krasnosel'skii fixed point theorem and the method of the upper and lower solutions.