Solvability for time‐fractional semilinear parabolic equations with singular initial data

Abstract

We discuss the existence and nonexistence of a local and global‐in‐time solution to the fractional problem where is a bounded domain with boundary, , and ( ) is the Caputo fractional derivative. We assume that is a continuous function such that for some , one has for all . Particular attention is paid to the doubly critical case .