Study On The Existence Of Solutions Of Conformable Fractional Differential Equations With Riemann-Stielties Integral Conditions

With the emergence of calculus,differential equations have gradually developed.In recent years,a large number of problems have occurred in real life,and people need to use related theories and methods of differential equation initial value or boundary value problems to deal with and solve.Whether it is an ordinary differential equation or a fractional differential equation,the existence of solutions to problems with integral boundary condition has been studied in applied science and physics.Boundary value problems with integral condition in fractional differential equations have attracted widespread attention,making boundary value problems of differential equations with integral condition applicable to chemical engineering and population dynamics.The first chapter is the introduction,which focuses on the background of integral boundary value problems of fractional differential equations,and expounds the research status of integral boundary value problems of fractional differential equations at home and abroad,and explains the research value and necessity of this subject.The second chapter is preliminary knowledge,it is mainly the basic definitions,lemmas and theorems related to this paper.The third chapter introduces the existence of extremal solutions of conformable fractional differential equation with Riemann-Stieltjes integral conditionsWhere,? ?(0,1].The monotonic iterative and the upper and lower solutions are used in the proof process.In addition,an example is given to illustrate our main results.In chapter four,conformable fractional differential equation with Riemann-Stieltjes integral conditions is studied,trying to study the multiplicity of solutions using topological degree theory and upper and lower solutions.In addition,the fixed point theorem of the set-value increasing operator is also applied in the proof process.In chapter five,the uniqueness of the solution of conformable fractional differential equationwith deviating arguments is explored.Where,??(0,1],??C([0,T],[0,T]),f?C([0,T]×R×R,R),D? is the ?-order conformable differential,.With the help of the new comparison principle,the sequence is constructed by monotone iterative method and it converges uniformly to extreme solution of conformable fractional differential equation.In this process,we use the spectral theory of linear operator.In chapter six,it is mainly the summary and prospect of this paper.