  This paper is devoted to the study of initial-boundary value problems for
time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers,
Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional
modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient
conditions for the blowing-up of solutions in finite time of aforementioned
equations are presented. We also discuss the maximum principle and influence of
gradient non-linearity on the global solvability of initial-boundary value
problems for the time-fractional Burgers equation. The main tool of our study
is the Pohozhaev nonlinear capacity method. We also provide some illustrative
examples.
