Existence And Uniqueness Of Solutions For Nonlinear Fractional Differential Equations

In recent years,fractional order calculus has been playing a more and more important role in many fields,and it has become the focus of research in many mathematical fields,and the existence and uniqueness of solutions have become the main research object.In this paper,the first chapter introduces the research background of fractional differential equations.The second chapter introduces the research of the existence and uniqueness of solutions of a class of 1-2 order nonlinear fractional differential equations by Guotao Wang et al.:where x₀^*,x₀?R,t?J:=[0,T]?T>0?,f?C?J x R x R,R?,0<q<1.Based on this,the third and the fourth chapters use the monotone iterative techniques and upper and lower solutions,and then solve the initial value problem of a class of nonlinear fractional differential equations of 2-3 order and 3-4 order by using a comparison principle,and obtain the result of the existence of extremal solutions of the initial problem.The first equations is where x₀^*,x₀?R,t?J:[0,T]?T>0?,f?C?J×R×R×R,R?,1<?<q<2.The second equations is where x₀^*,x₀?R,t ?J:=[0,T]?T>0?,f?C?J×R×R×R×R,R?,2<?<?<q<3.