Citation: | XU Jianzhong, MO Jiaqi. Asymptotic Solution for Fractional-Order 2-Parameter High-Order Nonlinear Perturbed Models[J]. Applied Mathematics and Mechanics, 2020, 41(6): 679-686. doi: 10.21656/1000-0887.400238 |
[1] |
DELBOSCO D. Existence and uniqueness for nonlinear fractional differential equation[J]. Journal of Mathematical Analysis and Applications,1996,204(2): 609-625.
|
[2] |
DE JAGER E M, JIANG Furu. The Theory of Singular Perturbation [M]. Amsterdam: North-Holland Publishing Co, 1996.
|
[3] |
BARBU L, MOROSANU G. Singularly Perturbed Boundary-Value Problems [M]. Basel: Birkhauserm Verlag AG, 2007.
|
[4] |
CHANG K W, HOWES F A. Nonlinear Singular Perturbation Phenomena: Theory and Applications [M]. New York: Springer-Verlag, 1984.
|
[5] |
MARTINEZ S, WOLANSKI N. A singular perturbation problem for a quasi-linear operator satisfying the natural condition of Lieberman[J]. SIAM Journal on Mathematical Analysis,2009,41(1): 318-359.
|
[6] |
TIAN C, ZHU P. Existence and asymptotic behavior of solutions for quasilinear parabolic systems[J]. Acta Applicandae Mathematicae,2012,121(1): 157-173.
|
[7] |
KELLOGG B, KOPTEVA N. A singularly perturbed semilinear reaction-diffusion problem in a polygonal domain[J]. Journal of Differential Equations,2010,248(1): 184-208.
|
[8] |
SAMUSENKO P F. Asymptotic integration of degenerate singularly perturbed systems of parabolic partial differential equations[J]. Journal of Mathematical Sciences,2013,189(5): 834-847.
|
[9] |
SKRYNNIKOV Y. Solving initial value problem by matching asymptotic expansions[J]. SIAM Journal on Applied Mathematics,2012,72(1): 405-416.
|
[10] |
MO J Q, CHEN X F. Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation[J]. Chinese Physics B,2010,19(10): 100203.
|
[11] |
MO J Q, LIN W T. A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation[J]. Acta Mathematicae Applicatae Sinica,2006,22(1): 27-32.
|
[12] |
MO J Q. A class of singularly perturbed differential-difference reaction diffusion equation[J]. Advances in Mathematics,2009,38(2): 227-231.
|
[13] |
MOJ Q. Homotopic mapping solving method for gain fluency of a laser pulse amplifier[J]. Science in China,2009,52(7): 1007-1010.
|
[14] |
MO J Q, LIN W T. Asymptotic solution of activator inhibitor systems for nonlinear reaction diffusion equations[J]. Journal of Systems Science and Complexity,2008,21(1): 119-128.
|
[15] |
MO J Q. Approximate solution of homotopic mapping to solitary wave for generalized nonlinear KdV system[J]. Chinese Physics Letters,2009,26(1): 010204.
|
[16] |
MO J Q. Singularly perturbed reaction diffusion problem for nonlinear boundary condition with two parameters[J]. Chinese Physics Letters,2010,19(1): 010203-010204.
|
[17] |
MO J Q, LIN W T. Generalized variation iteration solution of an atmosphere-ocean oscillator model for global climate[J]. Journal of Systems Science & Complexity,2011,24(2): 271-276.
|
[18] |
莫嘉琪, 林万涛, 杜增吉. 双参数非线性高阶椭圆型方程的奇扰动解[J]. 系统科学与数学,〖STHZ〗 2013,33(2): 217-221.(MO Jiaqi, LIN Wantao, DU Zengji. A singularly perturbed solution for nonlinear higher order elliptic equations with two parameters[J]. Journal of Systems Science and Mathematical Sciences,2013,33(2): 217-221.(in Chinese))
|
[19] |
XU J Z, ZHOU Z F. Existence and uniqueness of anti-periodic solutions for a kind of nonlinear nth-order differential equation with multiple deviating arguments[J]. Ann Diff Eqn, 2012,28(1): 105-114.
|
[20] |
XU J Z, MO J Q. The solution of disturbed time delay wind field system of ocean[J]. Acta Sci Natur Univ Nankaiensis,2019,52(1): 59-67.
|
[21] |
徐建中, 莫嘉琪. 一类流行性病毒传播的非线性动力学系统[J]. 南京理工大学学报, 2019,43(3): 286-291.(XU Jianzhong, MO Jiaqi. A class of nonlinear dynamic system of human groups for epidemic virus transmission[J]. Journal of Nanjing University of Science and Technology,2019,43(3): 286-291.(in Chinese))
|
[22] |
徐建中, 莫嘉琪. Fermi气体光晶格奇摄动模型的渐近解[J]. 吉林大学学报, 2018,56(6): 1-6.(XU Jiazhong, MO Jiaqi. Asymptotic solution of singular perturbation model for the Fermi gases optical lattices[J]. Journal of Jilin University,2018,56(6): 1-6.(in Chinese))
|
[23] |
冯依虎, 陈怀军, 莫嘉琪. 一类非线性奇异摄动自治微分系统的渐近解[J]. 应用数学和力学, 2018,〖STHZ〗 39(3): 355-363.(FENG Yihu, CHEN Huaijun, MO Jiaqi. Asymptotic solution to a class of nonlinear singular perturbation autonomic differential system[J]. Applied Mathematics and Mechanics,2018,39(3): 355-363.(in Chinese))
|
[24] |
史娟荣, 朱敏, 莫嘉琪. 一类Fermi气体光晶格非线性轨线模型[J]. 应用数学和力学, 2017,38(4): 477-485.(SHI Juanrong, ZHU Ming, MO Jiaqi. Study on path curves of a class of Fermi gases in optical lattices with nonlinear mechanism[J]. Applied Mathematics and Mechanics,2017,38(4): 477-485.(in Chinese))
|