【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-αu（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.更多还原

【Abstract】 The existence and the iterative method of solutions are studied for the nonlinear fractional differential equation D^αu（t） = f（t,u（t））,0 < t ≤ 1,t^1-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.更多还原