Lower Bounds of Blow-Up Time for Certain Fractional Diffusion Equations and Systems with Nonlinear Memory Terms in Bounded Domains

In this paper, we prove the lower bounds of the blow-up time of solutions for certain Caputo time fractional diffusion equations and systems with nonlinear memory terms under homogeneous Dirichlet boundary conditions. The proofs of our results rely on the auxiliary function method, the differential inequality technique, and the properties of the solutions of fractional differential inequalities.