Complex Order Calculus And Is Application

In this paper,we have studied the Riemann-Liouville type calculus,H and L-type Calculus and Weyl calculus in solving complex differential equations,and some results have been obtained.The article consists of four chapters.The first chapter is the introduction,which mainly introduces the research background of the article,briefly summarizes the main contents of the complex-order derivatives and the symbols,the basic conceptions of different type of complex-order calculus.The second chapter mainly introduces the H-type and L-type complex-order calculus,which is defined by integral path,and proves some properties of H-type calculus,and gives the solution of the special complex-order differenal calculus of H-type.The third chapter mainly studies the solution of R-L complex order differential equations in the form of z(2?),+az(?)+bz = c(t).It is reduced by the function matrix,and then solved by transforming into the second class of the Volterra integral equation.The fourth chapter gives the concept of ?-form solutions of complex differential equations,and particularly a kind of ?-form solution of the differential equation of the form t2z"(t)-(bt+c)z'(t)+ ?z(t)=0 is obtained by Weyl fractional integral.Further more,the necessary and sufficient conditions of the equation of this form possessing a polynomial solution are concluded.