Concavity in Fractional Calculus

We discuss a concavity like property for functions u satisfying D-0(+alpha) u is an element of 2 C[0; b] with u(0) = 0 and -D-0+(alpha) u(t) >= 0 for all t is an element of [0; b]. We develop the property for alpha 2 (1; 2], where D-0+(alpha) is the standard RiemannLiouville fractional derivative. We observe the property is also valid in the case alpha = 1. Finally, we show that under certain conditions, -D-0+(alpha) u(t) >= 0 implies u is concave in the classical sense.