期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

一类分数阶微分方程的本征值问题 被引量：2

Eigenvalue problems for a kind of fractional differential equations
下载PDF
导出
摘要 利用分数次导数的定义、分数算子的性质和Laplace变换,得到了一类分数阶微分方程本征值问题的本征值和本征函数. By means of the definition of fractional derivative, some properties of fractional operator and the Laplace transform, the eigenvalues and eigenvalue functions are obtained for a kind of eigenvalue problems of fractional differential equations.
作者 张淑琴 兰德品
机构地区 中国矿业大学(北京校区)数学系
出处 《西北师范大学学报（自然科学版）》 CAS 2006年第3期5-8,共4页 Journal of Northwest Normal University(Natural Science)
关键词 分数算子 分数阶微分方程 本征值问题 本征函数 LAPLACE变换 特殊函数 fractional operator fractional differential equation eigenvalue problem eigenvalue function Laplace transform special function
分类号 O175.1 [理学—基础数学]
  • 相关文献

参考文献8

  • 1MOUSTAFA L O. On the Cauehy problem for some fractional order partial differential equations [J].Chaos, Solitons, Fractals, 2003, 18: 135-140.
  • 2KOCHUBEI A N. A Cauchy problem for evolution equations of fractional order [J], Differential Equations, 1989, 25.. 967-974.
  • 3PSHU A V. Solutions of a boundary value problem for a fractional partial differential equation [J ].Differential Equations, 2003, 39(8) : 1150-1158.
  • 4ORSINGHER E, REGHIN L. Time- fractional telegraph equations and telegraph processes with Brownian time [J]. Probab Theory Relat Fields,2004, 128: 141-160.
  • 5张淑琴.有限区间上的分数阶扩散波方程的解[J].西北师范大学学报（自然科学版）,2005,41(2):10-13. 被引量：6
  • 6PODLUBNY I. Fractional Differential Equations[M]. San Diego: Academic Press, 1999.
  • 7SAMKO S G, KILBAS A A, MARICHEV O I.Fractional Integral and Derivatives ( Theorey and Applications)[M]. New York: Gordon and Breach,1993.
  • 8张淑琴.一类分数阶微分方程的本征值问题[J].兰州大学学报（自然科学版）,2005,41(3):98-101. 被引量：3

二级参考文献11

  • 1Kilbas A A, Pierantozzi T, Trujillo J. On the solution of fractional evolution equations[J]. J Phy A: Math Gen,2004, 37: 3271-3283.
  • 2Podlubny I. Fractional Differential Equations[M]. San Diego: Academic Press, 1999.
  • 3Samko S G, Kilbas A A, Marichev O I. Fractional Integral and Derivatives (Theory and Applications)[M].Switzerland: Gordon and Breach, 1993.
  • 4Osama L Moustafa. On the cauchy problem for some fractional order partial differential equations[J]. Chaos, Solitons Fractals, 2003, 18: 135-140.
  • 5Kochubei A N. A Cauchy problem for evolution equations of fractional order[J]. Differential Equations, 1989, 25: 967-974.
  • 6Pshu A V. Solutions of a boundary value problem for a fractional partial differential equation[J]. Differential Equations, 2003, 39(8): 1150-1158.
  • 7Domenico Delbosco, Lui Rodino. Existence and uniqueness for a nonlinear fractional differential equation[J]. J Math Appl, 1996, 204: 609-625.
  • 8Podlubny I. Fractional Differential Equations[M].San Diego: Academic Press, 1999.
  • 9Samko S G, Kilbas A A, Marichev O I. Fractional Integral and Derivatives (Theorey and Applications)[M]. New York: Gordon and Breach, 1993.
  • 10Enzo Orsingher, Luisa Reghin. Time-fracyinal telegraph equations and telegraph processes with brownian time[J]. Probab Theory Relat Fields, 2004,128: 141-160.

共引文献7

同被引文献11

  • 1Podlubny I. Fractional differential equations [J]. San Diego: Aca- demic Press, 1999.
  • 2Wu J L. A wavelet operational method for solving fractional partial differential equations numerically [J]. Applied Mathematics and Computation, 2009,214 (1): 31-40.
  • 3Chen Yiming, Wu Yongbing, Cui Yuhuan, et al.. Wavelet method for a class of fractional convection-diffusion equation with vari- able coefficients [J]. Journal of Computational Science, 2010,1 (3): 146-149.
  • 4Saadatmandi A, Dehghan M. A new operational matrix for solvingfractional-order differential equations [J]. Computers and Mathe- matics with Applications, 2010,59 (3): 1326-1336.
  • 5Canuto C, Hussaini M Y, Quarteroni A, et al.. Spectral methods in fluid dynamic [M]. Englewood Cliffs: Prentice-Hall, 1988.
  • 6E1-Mesiry A E M, E1-Sayed A M A, EI-Saka H A A. Numerical methods for multi-term fractional (arbitrary) orders differential equations [J]. Applied Mathematics and Computation, 2005,160 (3): 683-699.
  • 7Ford N J, Connolly J A. Systems-based decomposition schemesfor the approximate solution of multi-term fractional differential equations [J]. Journal of Computational and Applied Mathematics, 2009,229 (2): 382-391.
  • 8Chen C F, Hsiao C H. Design ofpiecewise constant gains for op- timal control via Walsh functions [J]. IEEE Transactions on Au- tomaticControl, 1975,20 (5): 596-603.
  • 9Wu J L, Hsiao C H. Haar wavelet method for solving lumped and distributed parameter systems [J]. IEE Proceedings-Control Theory and Applications 1997,144 (1): 87-94.
  • 10章红梅,刘发旺.一类特殊形式的时间分数阶Navier-Stokes方程的解[J].工程数学学报,2008,25(5):935-938. 被引量：2

引证文献2

二级引证文献1

西北师范大学学报（自然科学版）
2006年 第3期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部