- 期刊
Generalized Weber Equations via Fractional Calculus
利用分數微積分推廣Weber Equation
摘要
根據西本勝之教授分數微積分[1]，可獲得衆知的特殊二階微分方程式（如：Gauss, Legendre, Jacobi, Tchebycheff及Coulomb）的特解。 在參考文獻[2]-[7]中，一些學者再推廣上述各結果爲一般型並研論其特解。 最近，在1999年，於[8]，杜詩統教授等人又處理一般性的Associated Legendre, Euler，及Hermite的N階微分方程式的特解。在1998年，西本勝之教授，於[10]，採用N(上標 v)方法，獲得在量子力學上著名的Weber方程式的解。 本篇論文主要是推廣1998年西本勝之教授的結果，及研論一般型Weber方程式的特解，並舉例說明。
並列摘要
Based on Nishimoto's fractional calculus [1], the particular solutions to the well-known special second order differential equations, such as Gauss, Legendre, Jocobi, Tchebycheff, and Coulomb have been obtained. As for their generalized form, their particular solutions are discussed via fractional calculus method by some authors ([2]~[7]). Recently, in 1999, S.T.Tu, et al. [8] have treated the particular solution to the generalized Nth order equations, such as Associated Legendre, Euler, and Hermite equations. In 1998, K. Nishimoto [10], obtaincd a particular solution to the famous second order Weber cquation which appeared in quantum mechanics by using his N' method. In this paper, the solution to its generalized Weber equation by using fractional calculus method will be discussed in detail with some examples given.