具有脉冲和积分边值条件的分数阶微分方程的解

Solutions for Fractional Differential Equations with Impulsive and Integral Boundary Conditions

由于分数阶微分方程在实际应用中有着比整数阶微分方程更加广泛的范围.因此,提出及探讨了具有脉冲和非局部黎曼-刘维尔积分边值条件的分数阶微分方程解的存在唯一性问题,并使用分析技巧将问题转化成一个与之等价的积分方程,同时运用Schaefer不动点定理、Schauder不动点定理和Banach压缩映射原理得到解的存在唯一性的充分条件,然后举例验证了结论的有效性.

Compared with the integral differential equations,the fractional differential equations are more useful in reality,so the problem of fractional differential equations with impulsive and nonlocal Riemann-Liouville integral boundary conditions is proposed.With some analytical technique,the considered system is converted into an equivalent integral equation.Then by applying Schaefer's fixed point theorem,the Schauder fixed point theorem and Banach contraction principle,several sufficient conditions for the existence and uniqueness of the solutions are obtained.At last,the example is given to illustrate the effectiveness of the main results.