Biswas, Anup Lorinczi, Jozsef Maximum principles for time-fractional Cauchy problems with spatially non-local components We show a strong maximum principle and an Alexandrov-Bakelman-Pucci estimate for the weak solutions of a Cauchy problem featuring Caputo time-derivatives and non-local operators in space variables given in terms of Bernstein functions of the Laplacian. To achieve this, first we propose a suitable meaning of a weak solution, show their existence and uniqueness, and establish a probabilistic representation in terms of time-changed Brownian motion. As an application, we also discuss an inverse source problem. untagged;Mathematical Sciences not elsewhere classified 2018-11-08
    https://repository.lboro.ac.uk/articles/journal_contribution/Maximum_principles_for_time-fractional_Cauchy_problems_with_spatially_non-local_components/9376634