Hilfer左右混合分数阶微分方程边值问题解的存在性

Existence of Solutions for Boundary Value Problems of Hilfer Left and Right Mixed Fractional Differential Equations

在序Banach空间中构造合适的锥,通过运用五个泛函的不动点定理和φ—(g,e)—增凹算子的不动点定理,研究了一类新的具有左右Hilfer分数阶导数的混合微分方程边值问题,得到了该边值问题正解的多重性、存在唯一性的一些新结果;最后,将主要结果应用于两个具体实例,说明结论的正确性和适用性.

In this paper,we construct a suitable cone in ordered Banach space.By using the fixed point theorem of five functional and the fixed point theorem of concave increasing operator,we study a new class of boundary value problems for mixed differential equations with left and right Hilfer fractional derivatives,and obtain some new results on the multiplicity,existence and uniqueness of positive solutions of the boundary value problems;Finally,the main results are applied to two specific examples to illustrate the correctness and applicability of the conclusions.