Existence of weak solutions to nonlocal PDEs with a generalized definition of Caputo derivative

Abstract

Some compactness criteria that are analogies of the Aubin–Lions lemma for the existence of weak solutions of nonlinear evolutionary PDEs play crucial roles for the existence of weak solutions to time-fractional PDEs. Based on this fact, in this paper, we consider the existence of weak solutions to a kind of partial differential equations with Caputo time-fractional differential operator of order γ∈(0,1) and fractional Laplacian operator (−Δ)α , α∈(0,1).