Existence and regularity of final value problems for time fractional wave equations

Abstract

We study a class of final value problems for time fractional wave equations involvingCaputo’s fractional derivative of order 1<α<2 and a symmetric uniformly elliptic operator in a bounded domain Ω⊂RN, N=1,2,3. Firstly, we analyze the difficulties involved in the final value problem under consideration. Secondly, we establish the existence and uniqueness of the mild solution. Finally, we investigate the regularity of the mild solution in some special spaces.