2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/193362We consider FRW cosmology in non-local modified gravity. Its local scalar-tensor formulation is developed. It is explicitly demonstrated that such theory may lead to the unification of early-time inflation with late-time cosmic acceleration. The quintessence or phantom era may emerge for specific form of the action. The coupled non-local-F(R) gravity is also investigated. It is shown that such theory being consistent with Solar System tests may lead to the known universe history sequence: inflation, radiation/matter dominance and dark epoch.LaTeX file, 9 pages, version to appear in PLBHigh Energy Physics - TheoryAstrophysicsGeneral Relativity and Quantum Cosmologytext