NONEXISTENCE OF SOLUTIONS FOR TEMPERED FRACTIONAL PARABOLIC EQUATIONS

. In this paper, we consider the following parabolic equations involving tempered fractional operators. Assume that the function h is an element of C(R) to equation (1.1) is strictly increasing with respect to x1 and satisfying h(0) = 0. We use the method of moving planes to prove that all bounded positive solutions are strictly increasing in the x1 direction, and then based on this, we derive the non-existence of positive solutions. As a by-product, we also establish a maximum principle on unbounded domains for such a tempered fractional operator.