| 含Caputo分数阶导数的分数阶微分方程 |
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| 引用本文： | 段俊生.含Caputo分数阶导数的分数阶微分方程[J].天津科技大学学报,2003(Z1). |
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| 作者姓名： | 段俊生 |
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| 作者单位： | 天津商学院应用数学科学系 天津 |
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| 摘 要： | 求解了含Caputo分数阶导数的分数阶微分方程初值问题 d~αu/dtα+ω~αu(t;α)=h(t),t>0,0≤n-1<α≤n,ω>0, u~(k)(0~+;α)=u_k,k=0,1,…,n-1.利用Laplace变换方法和广义 Mittag-Leffler函数,得到其解为u(t;α)=integral from n=0 to t (r~(α-1)E_α,α(-(ωτ)~α))h(t-τ)dτ+sum from k=0 to n-1 u_kt~kE_(α,1+k)(-(ωt)~α)。
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| 关 键 词： | 分数阶积分 分数阶导数 广义Mittage-Leffler函数 Laplace变换 |
FRACTIONAL DIFFERENTIAL EQUATIONS WITH CAPUTO FRACTIONAL DERIVATIVES |
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| DUAN Jun-sheng Science of Applied Mathematics.FRACTIONAL DIFFERENTIAL EQUATIONS WITH CAPUTO FRACTIONAL DERIVATIVES[J].Journal of Tianjin University of Science & Technology,2003(Z1). |
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| Authors: | DUAN Jun-sheng Science of Applied Mathematics |
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| Institution: | DUAN Jun-sheng Science of Applied Mathematics Department,Tianjin University of Commerce,Tianjin 300134,China |
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| Abstract: | |
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| Keywords: | Fractional integral Fractional derivative Generalized Mittag-Leffler function Laplace transform |
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