Fractional galactic-halo wormholes and self-interacting scalar-field scattering: a q -HATM analysis

In this paper, we revisit the galactic-halo wormhole of Rahaman et al. (Eur. Phys. J. C 74, 2750, 2014) [1] and solve a genuine nonlinear problem having Liouville–Caputo fractional operator on the resulting background with the [Formula: see text]-homotopy analysis transform method. Two coupled results are reported. First, the fractional shape-function equation [Formula: see text] = [Formula: see text] is solved in closed series form and is shown to reduce exactly to the integerorder halo shape function at [Formula: see text] = 1. We make explicit that this equation is linear, that its effective source density for [Formula: see text] < 1 is a fractional derivative of the observed profile, and that dimensional homogeneity requires a length scale [Formula: see text]. Second, we place a self-interacting massless scalar field on this background. Near throat, its radial equation is a fractional Duffing equation [Formula: see text], for which the presented scheme produces non-trivial homotopy polynomials and a non-terminating series. Its convergence is controlled through the ħ and [Formula: see text]-parameters, the latter enlarging the convergence region since the term ratio obeys [Formula: see text]. The traversable geometry (throat, flare-out, null-energy-condition violation, positive active mass) survives for all [Formula: see text], and the fractional order leaves a measurable imprint on the near-throat scalar amplitude, giving the model an [Formula: see text]-dependent observable.