摘要
研究了非线性分数微分方程D~αu(t)=f(t,u(t)),0≤t≤1,t^(1-α)u(t)|t=0=c解的存在性与迭代方法,其中0<α<1.当c≠0时该方程的解是奇异的.通过构造了两个在Banach空间C_α[0,1]中收敛于解的逐次迭代序列证明了解的存在性.这项工作改进了文献[8]的主要结论.
The existence and the iterative method of solutions are studied for the nonlinear fractional differential equation Dαu(t) = f(t,u(t)),0 t ≤ 1,t1-αu(t)|t=o = c,where 0 α 1.The solutions of the equation are singular if c ≠ 0.By constructing two successively iterative sequences which converge to the solutions in the Banach space C_α[0,1],the existence of solutions is proved.The main result in[8]is improved by this work.
出处
《数学物理学报(A辑)》
CSCD
北大核心
2016年第2期287-296,共10页
Acta Mathematica Scientia
关键词
非线性分数微分方程
单调迭代方法
存在性
收敛速度
Nonlinear fractional differential equation
Monotone iterative method
Existence
Convergence rate