基于P_(h,e)下Riemann-Liouville分数阶微分方程解的存在唯一性

Existence and Uniqueness of Solutions for a Class of Riemann-Liouville Fractional Differential Equation based on set P_(h,e)

利用基于集合P_(h,e)上的一类混合单调算子不动点定理,研究了一类Riemann Liouville分数阶微分方程两点边值问题,获得了这类方程在集合P_(h,e)中解的存在性与唯一性,并用一组单调迭代序列逼近了该方程的唯一非平凡解.最后,利用一个实例验证了主要结论.

Based on a class of mixed monotone fixed point theorems on the set P_(h,e),the twopoint boundary value problem of a class of Riemann-Liouville fractional differential equations is studied in this paper.The existence and uniqueness of the solution in the set P_(h,e) are obtained,and the unique nontrivial solution of the equation is approximated by a set of monotone iterative sequences.Finally,an example is used to verify the main conclusion.