分数阶积分方程的小波解法-基础数学专业论文.docxVIP

Abstract Fractional calculus in the area of science and engineering is a very useful mathematical tool,for ex- ample in the flabby,concussion,control system,the diffusion and transport theories,viscoelastic mechanics and non-newtonian fluid mechanics,electrode-electrolyte polarization,pipe of the boundary layer effects and many other fields to application,they all establish fractional calculus mathematical model using frac- tional integrals.Many numerical solution of fractional integral equation methods also arises.However,the literature of fractional order integral equation using wavelet analysis to solve is seldom. Haar wavelets,Legendre wavelets and Chebyshev wavelets are all the nature of very good class of wavelets,they have fast convergence when expand function.Integral equations are divided into two cat- egories:The form of Fredholm integral equation and Volterra integral equations,While the former is the special case of the latter,for Fredholm equation,the kind of the second equation solution theory relatively complete,completly,and the theory of the first kind equations is incomplete.For Voiterra equation,in many cases,the first kind of equation can be reduced to the second kind,so the theory of these two kinds of equa- tion is no essentially difference. the wavelet method for solving Fredholm fractional integral equations are generally converted into Volterra fractional integral equation to solve. So this paper considered using the wavelets method for solving integral equation method to solve the type of Volterra fractional integral equation. This paper is divided into five parts. In the second chapter studied the fractional integral equation of the existence and uniqueness of the solution. In the third chapter we first give the method of Haar wavelet of solving fractional integral equa- tion,then we use the wavelet collocation method and Galerkin method to solve the linear and nonlinear Volterra fractional integral equation respectively. The fourth chapt