Fractional Sobolev Spaces and Variational Problems with Variable-Order Operators on Time Scales

Hafida Abbas, Abdelhalim Azzouz

We construct fractional Sobolev spaces on arbitrary time scales, both in one dimension and on product time scales. In 1D, we define $W_{\mathrm{rd}}^{\hat{I}\pm (\cdot ),p}(\mathcal{I})$ thro…