具有非分离边界条件的非线性分数阶微分包含弱解的存在性

摘要

Many practical problems, such as those from physics, aerospace science, ecological science and engineering, need to be described by fractional differential equations, so it is important to study these equations in theory and implement. In this paper, under the Pettis integrability assumption, we discuss the existence of weak solution to the boundary value problem for a class of nonlinear fractional differential inclu-sion involving non-separated boundary conditions. The differential operator is the Caputo derivative, and the nonlinear term has weakly sequentially closed graph. The analysis relies on Monch’s fixed point theorem combined with the technique of measures of weak noncompactness. Finally, an example is given to illustrate the effectiveness of the proposed method.%许多物理、航天科学、生态科学、工程中的实际问题都需要用分数阶微分方程来描述，因此对于分数阶微分方程的研究有着十分重要的理论意义和实践价值。本文在Pettis可积性假设条件下讨论了一类带有非分离边值条件的非线性分数阶微分包含弱解的存在性。微分算子是Caputo导算子，并且非线性项具有弱序列闭图像。本文的理论分析基于Monch不动点定理和弱非紧性测度的技巧，并举例论证了结论的有效性。