  We study acceleration phenomena in monostable integro-differential equations
with ignition nonlinearity. Our results cover fractional Laplace operators and
standard convolutions in a unified way, which is also a contribution of this
paper. To achieve this, we construct a sub-solution that captures the expected
dynamics of the accelerating solution, and this is here the main difficulty.
This study involves the flattening effect occurring in accelerated propagation
phenomena.
