Fractional index convolution complementarity problems

Convolution complementarity problems have the form: given a kernel function k and a function q, find a function u such that u(t)≥0, (k∗u)(t)+q(t)≥0 for (almost) all t, and where ∫0Tu(t)T[(k∗u)(t)+q(t)]dt=0. A fractional index problem of this kind has k(t)∼K0tα−1 for t small, with 0<α<1. Such problems are shown to have unique solutions under mild conditions.