Weak/mild solutions to the space‐fractional wave equation

Abstract In this paper, we study the space‐fractional wave equation Under suitable conditions, we prove that any non‐negative weak solution is identically zero when . Moreover, we show that no positive weak solution satisfying certain space‐Morrey type conditions exists for some . Additionally, we establish the existence of a mild solution for certain values of when , provided that the initial data and are sufficiently small.