采用拟线性化方法讨论了含causal算子的分数阶非线性微分方程初值问题,通过构造2个单调迭代序列,证明了它们一致且平方收敛于给出问题的解.
[1] 王培光, 高玮, WANG Pei-guang, GAO Wei. 集值微分方程初值问题的拟线性化方法 [J]. 河北大学学报(自然科学版) 2011.doi:10.3969/j.issn.1000-1565.2011.01.001
[2] LAKSHMIKANTHAM V, VATSALA A S. Generalized quasilinearization for nonlinear problems [M]. Dordrecht:kluwer Academic Publishers 1998.
[3] LAKSHMIKANTHAM V, LEELA S, DRICI Zah. Theory of causal differential equations [M]. World Scientific:Atlantis Press 2009.
[4] Fengjie Geng. Differential equations involving causal operators with nonlinear periodic boundary conditions [J]. Mathematical and computer modelling 2008, 5/6(5/6).
[5] Jankowski T. Boundary value problems with causal operators [J]. Nonlinear Analysis: An International Multidisciplinary Journal 2008, 12(12).
[6] Diethelm K., Ford NJ.. Analysis of fractional differential equations [J]. Journal of Mathematical Analysis and Applications 2002, 2(2).
[7] CAPUTO M. Linear models of dissipation whose Q is almost independent Ⅱ [J]. Geophys J R Astron 1967, 13(05).
[8] VASNUDHARA DEVI J, MCREA F A, DRICI Z. Generaized quasilinearization for fractional differential equations [J]. Computers and Mathematics with Applications 2010, 59(03).
[9] J. VASUNDHARA DEVI, CH. SUSEELA. Quasilinearization For Fractional Differential Equations [J]. Communications in applied analysis 2008, 4(4).
[10] J. VASUNDHARA DEVI. Generalized Monotone Method For Periodicboundary Value Problems Of Caputo Fractional differential Equations [J]. Communications in applied analysis 2008, 4(4).
