带有参数和含有p-Laplacian算子的混合型分数阶微分系统正解的唯一性

Uniqueness of positive solutions for mixed fractional differential systems with p-Laplacian operators and parameters

分析了一类带有p-Laplacian算子的混合型分数阶微分系统边值问题,其边界条件含有参数,且对参数具有一定的依赖性。利用格林函数的性质和半序Banach空间中两个算子之和的不动点定理,推导出正解的唯一性,并构造相应的迭代序列来逼近唯一正解。最后,给出两个数值应用实例验证主要结果的可行性。

This paper analyzes the boundary value problems of a class of mixed fractional differential systems with p-Laplacian operators,whose boundary conditions contain and are dependent on parameters.By using the properties of Green functions and the fixed point theorem of sum of two operators in semi-ordered Banach spaces,the uniqueness of the positive solution is derived and the corresponding iterative sequence to approximate the unique positive solution is constructed.Finally,two numerical examples are given as applications to demonstrate the feasibility of the main results.