一个非线性分数微分方程奇异解的存在性与逐次迭代方法

Abstract

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=0=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.

Key words: Nonlinear fractional differential equation, Monotone iterative method, Existence, Convergence rate

CLC Number:

O175.8

Yao Qingliu. Existence and Successively Iterative Method of Singular Solution to a Nonlinear Fractional Differential Equation[J].Acta mathematica scientia,Series A, 2016, 36(2): 287-296.

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References

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Existence and Successively Iterative Method of Singular Solution to a Nonlinear Fractional Differential Equation

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