BLOW UP RESULTS FOR FRACTIONAL DIFFERENTIAL EQUATIONS AND SYSTEMS

Abstract

The aim of this research paper is to establish sufficient conditions for the nonexistence of global solutions for the following nonlinear fractional differential equation D �|t u + (−�) �/2 |u| m 1 u + a(x) � ∇|u| q 1 u = h(x,t)|u| p , (t,x) ∈ Q, u(0,x) = u0(x), x ∈ R N where (−�) �/2 , 0 < � < 2 is the fractional power of −�, and D �|t , (0 < � < 1) denotes the time-derivative of arbitrary � ∈ (0;1) in the sense of Caputo. The results are shown by the use of test function theory and extended to systems of the same type.