具有积分边界条件的耦合φ-Hilfer分数阶微分系统解的存在性

Existence of solutions of coupled φ-Hilfer fractional differential systems with integral boundary conditions

为了拓展分数阶微分方程系统的相关理论,研究了一类具有积分边界条件的耦合φ-Hilfer分数阶微分系统。首先,将具有积分边界条件的耦合φ-Hilfer分数阶微分系统转化为积分系统;其次,定义合适的Banach乘积空间和范数,构造合适的积分算子,分别运用压缩映像原理和Kransnoselskii不动点定理得出耦合φ-Hilfer分数阶微分系统在积分边界条件下解的存在性结果;最后,通过列举实例说明所得结论的正确性。研究表明,积分边界条件下的耦合φ-Hilfer分数阶微分系统的解具有存在性。研究结论丰富了耦合分数阶微分系统理论可解性的相关理论,可为深入研究分数阶微分方程提供一定的理论参考。

In order to expand the relevant theory of fractional differential equation systems,a class of coupled φ-Hilfer fractional differential systems with integral boundary conditions was studied.Firstly,the coupled φ-Hilfer fractional differential system with integral boundary conditions was transformed into an integral system.Secondly,the appropriate Banach product space and norm were defined,the appropriate integral operator was constructed,and the existence result of the solution of the coupled φ-Hilfer fractional differential system under the integral boundary condition was given by using the compressed image principle and Kransnoselskii's fixed point theorem,respectively.Finally,examples were given to illustrate the correctness of the conclusions obtained.The results show that the solutions of the coupled φ-Hilfer fractional differential system under the integral boundary condition exist.The existence of solutions of coupled φ-Hilfer fractional differential systems is studied for the first time by using the compressed image principle and Kransnoselskii's fixed point theorem,respectively,and some innovative new results are obtained.In addition,the research conclusion enriches the relevant theories of the theoretical solvability of coupled fractional differential systems,and provides certain theoretical reference value for the further study of fractional order differential equations.