Existence And Multiplicity Of Solutions For Several Kinds Of Damped Impilsive Fractional Differential Equaions BVP

Fractional differential equations are generalizations of integerorder differential equations.They have received wide attention in recent years because they can more accurately describe many physical phenomena.Impulsive differential equation describes the physical phenomena that change or jump rapidly at a fixed time,and it has a wide range of applications in real life.Based on this,the existence and multiple solutions pf boundary value problems for several classes of impulsive fractional differential equations with damping terms are studied by using morse theory and critical point theory,and the sufficient conditions to guarantee the existence of solutions are given.An example is given to illustrate the validity and rationality of the given conditions.Firstly,this paper introduces the development history and research background of fractional calculus,and briefly describes the main research contents of this paper.Then,we select the appropriate workspace and give the corresponding variational structure of the problem.By using the critical point theorem,we give the criteria for the existence and multiplicity of solutions of boundary value problems for impulsive fractional differential equations with nonlinear damping terms.