论文标题
通过Riemann $ - $ $ $ $ liouville衍生产品按时间尺度及其应用于时间尺度的分数边界价值问题的左手Sobolev空间
Left fractional Sobolev space via Riemann$-$Liouville derivatives on time scales and its application to a fractional boundary value problem on time scales
论文作者
论文摘要
We first prove the equivalence of two definitions of Riemann-Liouville fractional integral on time scales, then by the concept of fractional derivative of Riemann-Liouville on time scales, we introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones on time scales.接下来，我们证明了引入空间中某些规范的等效性，并得出它们的完整性，反射性，可分离性和一些嵌入式。最后，作为应用程序，使用山间定理和属特性构造适当的变分设置，研究了一类Kirchhoff型分数P-Laplacian Systems的弱解决方案的存在，并研究了边界条件的时间尺度，并且获得了此问题弱解决方案的三个结果。
We first prove the equivalence of two definitions of Riemann-Liouville fractional integral on time scales, then by the concept of fractional derivative of Riemann-Liouville on time scales, we introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones on time scales. Next, we prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability and some imbeddings. Finally, as an application, by constructing an appropriate variational setting, using the mountain pass theorem and the genus properties, the existence of weak solutions for a class of Kirchhoff-type fractional p-Laplacian systems on time scales with boundary condition is studied, and three results of the existence of weak solutions for this problem is obtained.
