Maximal regularity for fractional difference equations of order 2<alpha<3 on UMD spaces

In this article, we study the \(^p\)-maximal regularity for the fractional difference equation Δαu(n)=Tu(n)+f(n), (n∈ N₀). We introduce the notion of \(α\)-resolvent sequence of bounded linear operators defined by the parameters \(T\) and \(α\), which gives an explicit representation of the solution. Using Blunck's operator-valued Fourier multipliers theorems on \(^p(Z; X)\), we give a characterization of the \(^p\)-maximal regularity for \(1 < p < ∞\) and \(X\) is a UMD space. For more information see https://ejde.math.txstate.edu/Volumes/2024/20/abstr.html