Hölder Continuous Solutions for Tempered Fractional Equations and Maximal Regularity

We characterize the Hölder regularity in time of classical solutions for a class of nonlocal abstract equations in terms of resolvent estimates of the underlying operator, thus including in our approach those recently incorporated into the literature that study nonlocal versions of the Moore-Gibson-Thompson equation. This allows us to prove new maximal regularity results, including a priori estimates. Our results are flexible enough to allow the admissibility of operators other than the Laplacian. Furthermore, the presented method is reliable enough to apply these techniques to other nonlocal abstract equations of interest, obtain similar results and promote new findings. © The Author(s) 2025.