The Harnack inequality for the Riemann-Liouville fractional derivation operator

Abstract

In this note we establish the Harnack inequality for the Riemann-Liouville fractional derivation operator ∂ t of order α ∈ (0, 1). Here the function under consideration is assumed to be globally nonnegative. We show that the Harnack inequality in general fails if this global positivity assumption is replaced by a local one. A Harnack estimate is also derived for nonnegative solutions of a class of nonhomogeneous fractional differential equations. AMS subject classification: 26A33, 45D05, 47G20