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題 名 | On the Fractional Calculus(e礼戸(z-a)[fef5])β)α)and (((z-a)[fef5])β.e )α=利用分數微積分研討(e礼戸.((z-a)[fef5])β)α)and (((z-a)[fef5])β.e礼戸)α |
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作 者 | 杜詩統; 呂幸華; 黃郁丹; | 書刊名 | 中原學報 |
卷 期 | 27:1 1999.03[民88.03] |
頁 次 | 頁7-10 |
分類號 | 314.1 |
關鍵詞 | 分數微積分; 高斯超幾何函數; 萊不尼茲法則; 合流超幾何函數; Pochhammer符號; Fractional calculus; Gauss hypergeometric function; Leibniz rule; Pochhammer symbol; Confluent hypergeometric function; |
語 文 | 英文(English) |
中文摘要 | 在很多有關分數微積分旳文章裡,對任一個函數的分 數微分或積分,我們發現這領域上一些有系統的結論,並可 應用在常微分方程式、偏微分方程式、特殊方程式,以及積 分方程式上。 在參考文獻[1]中記載著西本勝之教授所發表的分數微 積分,根據這個理論,在1993年西本勝之教授與杜詩統教 授研論對兩個代數函數乘積的分數微分與積分[2]。上述的著 作中在討論Gauss,Bessel,Whittaker,Jacobi,Gegenbauer 及Tchebycheff方程式的解時,採用高斯超幾何函數來表示 其解。處理這一類問題時,分數微積分是一種既簡單又明瞭 的工具。 最近,於[3]杜詩統教授等人又進一步的將[2]推廣,及 在1997年西本勝之教授討論指數函數與代數函數乘積的微 分與積分[8]。 而本篇論文主要的在推廣上述1997年西本勝之教授的 結果,及更進一步的研論其交換性。 |
英文摘要 | In the significanlty vast literature on fractional calculus that is, differentiation and integration of an arbitrary real or complex order, we find many systematic (and historical) accounts of its theory and application in a number of areas including (for example) ordinary and partial differential equations, special function, and itegral equations. Based on Nishimoto's fractional calculus [1], in 1993, Nishimoto and S.T. Tu [2] presented the fractional calculus of the form ((z-a) . (z-b)) ��.Thse previous results are useful and simple tools for expressing the solutions of Gauss, Bessel. Whittaker, Jacobi, Gegenbauer and Tchebycheff equations ([4] ∼ [8}) in terms of the familier Gauss Hypergeometric function �� F �� (a,b:c:z). Recently, S.T. Tu et al. [3]showed the more generalized results of above mensioned forms. and in 1997, Nishimoto [8] gave a serendipity result in N-fractional calculus on (e . z �� ) and (z �鶠D e), The main object of our present paper is to extnd Nishimoto's results to more general forms. Some interesting examples are also given. |
本系統中英文摘要資訊取自各篇刊載內容。