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  本文關(guān)鍵詞：求分?jǐn)?shù)階偏微分方程精確解的兩類方法　出處：《江蘇大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 分?jǐn)?shù)階微分方程 擴(kuò)展的指數(shù)函數(shù)展開法 首次積分法 精確解

【摘要】：近年來,分?jǐn)?shù)階微分方程的應(yīng)用范圍已經(jīng)涉及到了生物工程、高能物理、系統(tǒng)控制、反常擴(kuò)散等諸多領(lǐng)域。然而關(guān)于分?jǐn)?shù)階微分方程的求解,目前并沒有統(tǒng)一的方法。因此,對分?jǐn)?shù)階微分方程進(jìn)行求解成為了一個(gè)熱門的研究領(lǐng)域。本文介紹了分?jǐn)?shù)階微積分的相關(guān)概念,并依據(jù)修改的Riemann-Liouville導(dǎo)數(shù)定義將分?jǐn)?shù)階微積分的理論應(yīng)用于分?jǐn)?shù)階微分方程的求解。文中對擴(kuò)展的指數(shù)函數(shù)展開法進(jìn)行了改進(jìn),并運(yùn)用該方法和首次積分法分別求解了分?jǐn)?shù)階Sharma-Tasso-Olever(STO)方程,分?jǐn)?shù)階Cahn-Allen(CA)方程和分?jǐn)?shù)階Whitham-Broer-Kaup(WBK)方程組,得到了三角函數(shù)、雙曲函數(shù)、有理函數(shù)、指數(shù)函數(shù)等各種類型的精確解。這些實(shí)例說明這兩種求解分?jǐn)?shù)階微分方程的方法具有很好的有效性和簡易性。
[Abstract]:In recent years, the application of fractional differential equations has been involved in many fields, such as bioengineering, high energy physics, system control, anomalous diffusion and so on. At present, there is no uniform method. Therefore, solving fractional differential equations has become a hot research field. In this paper, the concept of fractional calculus is introduced. The theory of fractional calculus is applied to the solution of fractional differential equations according to the modified Riemann-Liouville derivative definition. The extended exponential function expansion method is improved in this paper. The fractional Sharma-Tasso-OleverSTO equation is solved by using this method and the first integral method, respectively. The trigonometric function, hyperbolic function and rational function are obtained for the fractional Cahn-AllenCA equation and the fractional Whitham-Broer-Kaupn WBK equations. These examples show that the two methods for solving fractional differential equations are effective and simple.
【學(xué)位授予單位】：江蘇大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.2

【參考文獻(xiàn)】

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1 何雪s，

本文編號：1439288