Abstract fractional linear pseudo-parabolic equations in Banach spaces: well-posedness, regularity, and asymptotic behavior

Abstract

In this paper we study the well-posedness, regularity, and asymptotic behavior of the solutions \red{to} the \red{abstract} pseudo-parabolic equation $\partial_t^\alpha u(t) = A u(t) + B\partial_t^\beta u(t) + f(t),$ where $A,B$ are closed linear operators in a Banach space, and $\partial_t^\gamma u$ denotes the Caputo or Riemann--Liouville fractional derivative of order \red{$\gamma>0$.}