ZHU Zheng-you, LI Gen-guo, CHENG Chang-jun. A Numerical Method for Fractional Integral With Applications[J]. Applied Mathematics and Mechanics, 2003, 24(4): 331-341.
 Citation: ZHU Zheng-you, LI Gen-guo, CHENG Chang-jun. A Numerical Method for Fractional Integral With Applications[J]. Applied Mathematics and Mechanics, 2003, 24(4): 331-341.

A Numerical Method for Fractional Integral With Applications

• Rev Recd Date: 2003-01-06
• Publish Date: 2003-04-15
• A new numerical method for the liactional integral that only stores part history data is preseated, and its discretization error is estimated.The method can be used to solve the integno-diffemntial equation including fiactional integral or fractional derivative in a long history.The difficulty of storing all history data is overcoane and the error can be controlled. As application, motion equations goverring the dynandcal behavior of a viscoelastic Timoshenko beam with fractional derivative constitutiverelation are gniven.The dynamical response of the beam subjected to a periodic excitation is studied by using the separation variables metiwd. Then the new numerical method is used to solve a class of wealdy singular Voltena integro-differential equations which are applied to descaibe the dynamical behavior of viscoelastic beams with fractional derivative constitutive relations. The analytical and unmeiical results are compared.It is foiurd that they are very close.
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