We study the p(.) -> q(.) boundedness of weighted multidimensional Hardy-type operators H-w(alpha(.)) and H-w(alpha(.)) of variable order alpha(x), with radial weight w(vertical bar x vertical bar), from a variable exponent locally generalized Morrey space L-p(.),L-phi(.)(R-n, w) to another L-q(.),L-psi(.)(R-n, w). The exponents are assumed to satisfy the decay condition at the origin and infinity. ...