Uniform stability for fractional Cauchy problems and applications - Abadias, Luciano; Alvarez, Edgardo (Topological Methods in Nonlinear Analysis, 2018)
In this paper we give uniform stable spatial bounds for the resolvent operator families of the abstract fractional Cauchy problem on $\mathbb{R}_+$. Such bounds allow to prove existence and uniqueness of $μ$-pseudo almost automorphic $ε$-mild regular solutions to the nonlinear fractional Cauchy problem in the whole real line. Finally, we apply our main results to the fractional heat equation with critical nonlinearities.