Intrinsic {Right} $q$-Radial Vector Derivatives and Localized Fischer Decompositions on Radial Algebras
We define intrinsic right \(q\)-radial vector derivatives on radial algebras of abstract vector variables. For a finite parameter set \(Y\), a scalar Jackson calculus on \(x^2\) and the mixed anticommutators \(\{x,y_i\}\) is combined with the exterior decomposition relative to \(x\). Relabelling covariance and compatibility under inclusions of parameter sets give a direct-limit operator on arbitrary radial algebras. {Under the dimension specialization \(Q=q^M\), its classical limit agrees in every \(M\)-dimensional Clifford realization with the standard right Clifford derivative; for an exterior blade one obtains \([x\wedge y_I]\partial_x=(-1)^{|I|}(M-|I|)y_I\).} Two Fischer-type constructions are considered. The anticommutator with exterior creation is triangular and admits an explicit Green inverse after localization at its diagonal factors. {For right \(q\)-monogenic elements, the derivative is paired with right multiplication \(R_xF=Fx\). The homogeneous operators \(\partial^{Y,\mathrm R}_{x,q}R_x\) have generically nonzero determinants, which yields determinant-localized Fischer decompositions and explicit projectors.} The one- and two-vector determinants are computed explicitly. {After \(Q=q^M\), the two-vector determinant is nonzero for every \(0<q<1\) and every positive integer \(M\). For arbitrary finite support, a support filtration factors the determinant into exact-support terms; in degree zero, support rank \(p\) contributes the factor \([m-p]_q+p\).}