We consider the Cauchy problem of time fractional reaction-diffusion equation where 0 < α < 1, p > 1 and denotes the Caputo time fractional derivative of order α. The initial condition is assumed to be nonnegative and bounded continuous function. For the nondecaying initial data at space infinity, we show that the positive solution blows up in finite time and give the estimate of the life span of positive solutions. It is also given blow-up time of the solutions when the initial data attain its maximum at space infinity.
We consider the Cauchy problem of time fractional reaction-diffusion equation where 0 1 and denotes the Caputo time fractional derivative of order . The initial condition is assumed to be nonnegative and bounded continuous function. For the non-decaying initial data at space infinity, we show that the positive solution blows up in finite time and give the estimate of the life span of positive solutions. It is also given blow-up time of the solutions when the initial data attain its maximum at space infinity.