Research On The Existence Of Solutions To Boundary Value Problems Of Several Types Of Fractional Differential Equations

With the gradual improvement of nonlinear analysis theory,fractional calculus provides accurate tools for scientists in various fields due to its high accuracy and application.Because of its high accuracy and application,fractional calculus provides scientists with accurate tools in various fields.Fractional differentiation not only provides a theoretical basis for describing the genetic characteristics of various organisms and the memory of processes,but also can describe some physical phenomena better than integer differentiation,which has profound significance for solving practical problems.This paper mainly discusses the existence of positive solutions for several classes of nonlinear fractional differential equations,and some new results ara obtained.It contains the following four chapters:The first chapter is the introduction and gives the definition and lemma of fractionalorder differential equations.In the second chapter,we discuss a class of semipositone fractional differential equations with multi-point boundary value conditions By using fixed point index theorem,the existence of the positive solution is obtained.The third chapter,we investigate the existence for a class of higher-order fractional differential equation with integral boundary value conditions involving p-q–order derivatives As application of the height functions on some special bounded sets,the existence of two positive solutions is obtained by means of the Leray-Schauder nonlinear alternative and cone expansion and cone compression fixed point theory.The fourth chapter is to deals with the existence of multiple positive solutions for the following system nonlinear fractional differential equations multi-point boundary problems with p-Laplacian operator The existence and multiplicity of solutions are obtained by employing Leray-Schauder alternative theory and Leggett-Williams fixed point theorem.