- 作者: 杜詩統
- 作者服務機構: 中原大學應用數學研究所
- 中文摘要: 自1979年,日本大學西本勝之教授,利用歌西積分公式定義分數微積分以來,已經有三本專門著作(分別於1984年,1987年,1989年出版)專門討論其理論、性質、以及應用。在應用上不但可作為討論非齊次微分方程式之解的有效工具外,同時可以可微分積分函數表示其解。 利用分數微積分法於1991年曾探討過西本某微分方程式的解(參照與西本教授共著文獻1991a與1991b)並發表於日本大學數學雜誌上。本論文為更深一層的研究並推廣至更一般的型並討論其解。
- 英文摘要: Fractional calculus is a very useful and simple means of obtaining particular solutions to certainnon-homogeneous linear differential equations. The solutions of linear ordinary differential equations ofthe Fuchs type(Nishimoto, 1984, 1985, 1986, 1987a, 1987c,1989; Nishimoto and Kalla, 1989b; Nishimoto and Tu, 1989;Srivastava et al, 1985), Gauss type (Nishimoto, 1987b;Nishimoto and Tu, 1990)and Laguerre's type (Nishimoto and Kalla, 1989a) obtained by K. Nishimoto, S. L. Kalla, H. M. Srivastava,S. Owa, and S.T.Tu, are but a few important discoveries stemming from these researches. Recently, twogeneralizations of Nishimoto's third order ordinary differential equation of the Fuchs type have beenreported by the author and his colleagues (Nishimoto et al, 1991a, 1991b). In this paper one more genera-lization of the same third order differential equation obtained by Nishimoto is reported.
- 中文關鍵字: fractional calculus; fractional differintegral functions; non-homogenuous linear differential equations
- 英文關鍵字: --