In this paper, based on the developed nonlinear fourth-order operator and method of order reduction, a novel compact difference scheme is constructed for mixed-type time-fractional Burgers’ equation, from which L1-discretization formula applied to deal with terms fractional derivative, convection term discretized by operator. Then fully discrete L1 uniform meshes can be established approximatin...

We investigate a semilinear time-fractional damped wave equation in one dimension, posed bounded interval. The considered involves convection term and singular potentials on extremity of the A Dirichlet boundary condition depending time-variable is imposed. Using nonlinear capacity estimates, we establish sufficient conditions for nonexistence weak solutions to problem. In particular, when inde...