Existence Of Solutions For Few Kinds Of Dynamic Equation Of Boundary Value Problems On Time Scales

In this thesis,by using the fixed-point theory on cone,the existence and multiplicity of positive solutions of boundary value problems with conformable fractional derivative on time scales are considered and gives the corresponding Laplace transform.According to the content,the full text is divided into six chapters:In chapter one,we introduce the research background and development of boundary value problems of differential equations on time scales.The chapter two introduces the related definitions and lemmas of time scales.Through the calculation,we give the Green function of fractional differential equation boundary value problem with conformable fractional derivative.Give the Laplace transformation of linear homogeneous problem.And the two important theorems-uniform convergence theorem of the function family and fixed point theorem be proposed.In chapter three,we study the positive solutions of nonlinear boundary on time scales.At first,give the results,i.e.control the nonlinear term,use the cone fixed point theorem proving the existence and multiplicity of positive solutions of the problem.In chapter four,we research the positive solutions to boundary value problems of p-Laplacian with conformable fractional derivatives on time scales.The integral operator corresponding to the boundary value problem is given.By using the properties of the Laplace operator,we obtain the complete continuity of the integral operator,and then prove the existence and multiplicity of positive solutions of the problem by using the fixed point theorem.In chapter five,we research the existence of solutions to p-Laplacian difference equations under barrier strips conditions on time scales.It's important to find the priori bounds of the boundary value problems,then using the Leary-Schauder theorem can obtain the existence of the problem.The sixth chapter is the summary and prospect of this thesis.