重要的拉普拉斯变换公式及其应用  

Important Laplace Transform Formula and Its Application

作　　者：梁家辉 LIANG Jia-hui(School of Mathematics,Qilu Normal University,Ji'nan 250200,China)

机构地区：[1]齐鲁师范学院数学学院,山东济南250200

出　　处：《数学的实践与认识》2023年第9期230-256,共27页Mathematics in Practice and Theory

摘　　要：在公式L^(-1)[(s^(αγ-β)/S^(α)+α)^(γ)]=t^(β-1)E_(α,β)^(γ)(干at^(α))的基础上,对L^(-1)[s^(-β)(s^(α_(n))±a_(n-1)s^(α_(n-1))±…±a_(1)s^(α_(1))±a_0s^(α_(0)))^(-γ)](Re(γ)>0)进行研究和推广.通过数学归纳法和多项式展开定理得到L^(-1)[s-β/s^(-β)(s^(α_(n))±a_(n-1)s^(α_(n-1))±…±a_(1)s^(α_(1))±a_0s^(α_(0)))^(-γ)](Re(γ)>0)的通项式.最后,通过例子的应用,证实了结论的正确性.In this paper,L^(-1)[s^(-β)(s^(α_(n))±a_(n-1)s^(α_(n-1))±…±a_(1)s^(α_(1))±a_0s^(α_(0)))^(-γ)](Re(γ)>0)is studied and generalized on the basis of L^(-1)[(s^(αγ-β)/S^(α)+α)^(γ)]=t^(β-1)E_(α,β)^(γ)(干at^(α)).Use mathematical induction and polynomial expansion theorem to obtain the general formula L^(-1)[s-β/s^(-β)(s^(α_(n))±a_(n-1)s^(α_(n-1))±…±a_(1)s^(α_(1))±a_0s^(α_(0)))^(-γ)](Re(γ)>0)for Finally,the correctness of the conclusion is proved by an example.

关 键 词：LAPLACE变换 分数阶微分方程 CAPUTO分数阶导数 

分 类 号：O175[理学—数学]