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Caputo型分数阶微积分求解及其误差估计 被引量:1

Algorithm and Error Estimate on the Fractional Differential Equation With Caputo Derivative
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摘要 研究Caputo型分数阶微分函数的正解情况,考察其正解的唯一性问题,进而研究其数值求解的误差估计,所得结果拓展了Wyss的研究成果. The development speed of the reactional differential equation is slow due to the application nonlocality and the calculative complexity. In this paper, we will discuss the positive solution to the fractional differential equation with Ca- puto derivative based on the current research. Then we also study the uniqueness of the solution and discern the deviation comparing with numerical solution. The paper expands Wyss' research and conclusion.
作者 李瑾
出处 《华侨大学学报(自然科学版)》 CAS 北大核心 2015年第6期721-725,共5页 Journal of Huaqiao University(Natural Science)
基金 河南省2014年软科学研究计划项目(142400411076)
关键词 分数阶微积分 Caputo型 CHEBYSHEV多项式 误差估计 唯一性 fractional differential equation Caputo derivative Chebyshv polynomial error estimate uniqueness
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  • 1PODLUBNY L Fractional differential equations, mathematics in science and engineering[M]. New York: AcademicPress, 1996 : 120-125.
  • 2MILLER K S, Ross B. An introduction to the fractional calculus and fractional differential equations [M]. NewYorkjohn Wiley, 1998: 76-91.
  • 3HIEBER M Laplace transforms and crtime integrated semigroups[J]. Forum Math, 1991,120(3) : 595-612.
  • 4徐明瑜,谭文长.中间过程、临界现象——分数阶算子理论、方法、进展及其在现代力学中的应用[J].中国科学(G辑),2006,36(3):225-238. 被引量:34
  • 5DIETHELM K. An improvement of a nonclassical numerical method for the computation of fractional derivatives[J]. Numer Algor,2009,131(1) :209-254.
  • 6SUGIURA H,HASEGAWA T. Quadrature rule for Abel's equations; Uniformly approximating fractional deriva-tives[J]. Comput Appl Math,2009,223(1) :460-471.
  • 7FOX C. The G and H functions as summertrical Fourier kernels[J]. Trans Amer Math Soc,1961(98) :396-410.
  • 8ELLIOTT D. ELLIOTT Truncation errors in two Chebyshev series approximations [J]. Math Compute, 1965(19):234-248.
  • 9FUJITA Y. Fujita Cauchy problems of fractional order and stable processes[J]. Japan J Appl Math, 1990,7(3):459-476.
  • 10FUJITA Y. Integra differential equation which interpolates the wave equation[J]. Osaka J Math, 1990,116(27):797-804.

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