Uniform stability for fractional Cauchy problems and applications

Luciano Abadias, Edgardo Alvarez

DOI: http://dx.doi.org/10.12775/TMNA.2018.038


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 $\mu$-pseudo almost automorphic $\epsilon$-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.


Fractional Cauchy problem; uniform stability; $\mu$-pseudo almost automorphic functions; resolvent operator families; mild solutions

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