Multi-term time-fractional diffusion equation and system: mild solutions and critical exponents

The paper deals with a multi-term time-fractional semi-linear diffusion equation and system. Firstly, the existence of local mild solutions to the Cauchy problems for the multi-term time-fractional diffusion equation and system are proved. Also, we obtain Fujita-type and Escobedo—Herrero-type critical exponents for the multi-term time-fractional diffusion equation and system, respectively. It is shown that the nonexistence results of solutions depend on the order of the lowest derivatives of the multi-term time-fractional diffusion equation and system.