《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (6): 41-47.doi: 10.6040/j.issn.1671-9352.0.2019.757
• • 上一篇
安佳辉,陈鹏玉*
AN Jia-hui, CHEN Peng-yu*
摘要： 运用Schauder不动点定理,研究了变分数阶微分方程的初值问题{Dq(t)0+x(t)=f(t,x), 0
中图分类号:
| [1] KILBAS A A, SRIVASTAVE H M, TRUJILLO J J. Theory and applications of fractional differential equations[M]. Amsterdam: Elsevier Besloten Vennootschap, 2006. [2] LAKSHMIKANTHAN V, VATSALA A S. Basic theory of fractional differential equations[J]. Nonlinear Analysis, 2008, 69(8):2677-2682. [3] AGARWAL R P, BENCHOHRA M, HAMZNI S. Boundary value problems for fractional differential equations[J]. Georgian Mathematical Journal, 2009, 16(3):401-411. [4] SU Xinwei. Boundary value problem for a coupled system of nonlinear fractional differential equations[J]. Applied Mathematics Letters, 2009, 22(1):64-69. [5] ZHANG Shuqin. The existence of a positive solution for a nonlinear fractional differential equations[J]. Journal of Mathematical Analysis and Applications, 2000, 252(2):804-812. [6] MCRAE F A. Monotone iterative technique and results for fractional differential equations[J]. Nonlinear Analysis, 2009, 71(12):6093-6096. [7] YU Cheng, GAO Guozhu. Existence of fractional differential equations[J]. Journal of Mathematical Analysis and Applications, 2005, 31(1):26-29. [8] DENG J Q, MA L F. Existence and uniqueness of solutions of initial value problems for uniqueness fractional differential equations[J]. Applied Mathematics Letters, 2010, 23(6):676-680. [9] VALÉRIO D, COSTA J S. Variable-order fractional derivatives and their numerical approximations[J]. Signal Processing, 2011, 91(3):470-483. [10] LORENZOS C F, HARTIEY T T. Variable order and distributed order fractional operators[J]. Nonlinear Dynamics, 2002, 29(4):57-98. [11] SUN H G, CHEN W, WEI H, et al. Variable-order fractional differential operators in anomalous diffusion modeling[J]. Statistical Mechanics and its Applications, 2009, 388(21):4586-4592. [12] TSENG C C. Design of variable and adaptive fractional order FIR differentiators[J]. Signal Processing, 2006, 86(10):2554-2566. [13] RAZMINIA A, DIZAJI A F, MAJD V J. Solution existence for non-autonomous variable-order fractional differential equations[J]. Mathematical and Computer Modelling, 2012, 55(3):1106-1117. [14] LORENZO C F, HARTLEY T T. Variable order and distributed order fractional operators[J]. Nonlinear Dynamics, 2002, 29(4):57-98. [15] ZHANG Shuqin. Exisitence and uniqueness result of solutions to initial value problems of fractional differential equations of variable-order[J]. Journal of Mathematical Analysis and Applications, 2013, 4(1):82-98. [16] ZHANG Shuqin. The uniqueness result of solutions to initial value problems of differential equations of variable-order[J]. Rev R Acad Cienc Exactas Fís Nat Ser A Math, 2018, 112(2):407-423. |
| [1] | 陈彬. 格林函数变号的三阶周期边值问题[J]. 山东大学学报（理学版）, 2016, 51(8): 79-83. |
| [2] | 吴成明. 二阶奇异耦合系统正周期解的存在性[J]. 山东大学学报（理学版）, 2015, 50(10): 81-88. |
| [3] | 李娇. Caputo分数阶微分方程初值问题解的存在性与惟一性[J]. J4, 2013, 48(4): 60-64. |
| [4] | 王建国,刘春晗. Banach空间积-微分方程含间断项边值问题的解[J]. J4, 2013, 48(10): 18-22. |
| [5] | 陈建名,刘锡平*,肖羽. 半无穷区间上二阶微分方程积分边值问题多个正解的存在性[J]. J4, 2011, 46(4): 37-41. |
| [6] | 李耀红1,2,张海燕1. Banach空间中二阶非线性混合型积分-微分方程初值问题的解[J]. J4, 2010, 45(12): 93-97. |
| [7] | 娄国久 张兴秋 王建国. Banach空间一阶非线性混合型积微分方程正解的存在性[J]. J4, 2009, 44(8): 74-79. |
| [8] | 张明，路慧芹 . 二阶非线性脉冲周期边值问题多个正解的存在性[J]. J4, 2009, 44(4): 51-56 . |
| [9] | 王建国,高庆龄 . 奇性(k,n-k)共轭边值问题解的存在惟一性[J]. J4, 2008, 43(3): 43-47 . |
| [10] | 孟艳双,杨振起 . 一类概周期系数微分方程的概周期解[J]. J4, 2006, 41(5): 87-90 . |
|
||
