一类非线性分数阶微分方程组的爆破解

用Laplace变换法研究一类时间分数阶非线性微分方程组, 得到了与其等价的积分方程组. 结果表明, 积分方程组存在局部解. 用Hlder不等式估计非线性时间方程组,得到了该方程组具有有限时间的爆破解.

Blowing-up Solutions of a Type of Nonlinear System of Fractional Differential Equations

The authors focused on the study of a type of nonlinear system of time-fractional differential equations,and obtainsed the system of the integral equations which is equivalent to the system of nonlinear partial differential equations with time-fractional derivative via the approach of Laplace transformation,and proved the existence of local solutions to the system of the integral equations.In addition,we investigated the blowing-up solutions to the nonlinear system of fractional differential equations using Hlder’s inequality,and obtained the blowing-up solution of equation set in a finite time.