A Characterization of Lp-Maximal Regularity for Time-Fractional Systems in Umd Spaces and Applications

In this article we provide new insights into the well-posedness and maximal regularity of systems of abstract evolution equations, in the framework of periodic Lebesgue spaces of vector-valued functions. Our abstract model is flexible enough as to admit time-fractional derivatives in the sense of Liouville-Grünwald. We characterize the maximal regularity property solely in terms of R-boundedness of a block operator-valued symbol, and provide corresponding estimates. In addition, we show practical criteria that imply the R-boundedness part of the characterization. We apply these criteria to show that the Keller-Segel system, as well as a reactor model system, have Lq−Lp maximal regularity. © 2024 Elsevier Inc.