A fractional derivative of order 1/2. The semiderivative of t^λ is given by D^(1/2) t^λ = (t^(λ - 1/2) Γ(λ + 1))/(Γ(λ + 1/2)), so the semiderivative of the constant function f(t) = c is given by D^(1/2) c = clim_(λ->0) (t^(λ - 1/2) Γ(λ + 1))/(Γ(λ + 1/2)) = c/sqrt(π t).
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