Oxidative aging reduces the rheological performance of asphalt, resulting in increased stiffness and decreased viscoelasticity. Buton stone asphalt is a natural asphalt whose use requires a softening process. Natural asphalt softeners affect the properties of natural asphalt in asphalt-concrete mixtures. This study examined the use of used engine oil combined with crumb rubber and fly ash additives, which were reduced in size to the nanoscale and then tested using a dynamic shear rheometer to determine short- and long-term aging processes at 25–60 °C. The characteristics of the mixtures with these additives were evaluated in terms of the rut stiffness and fatigue resistance using the power law rheological model, which is a development of the power law. The results revealed a fourfold increase in stiffness. Moreover, the addition of nanoadditives increased the resistance to aging. A mixture of buton stone asphalt with nano crumb rubber and nano fly ash resulted in changes in the stiffness values ​​and structural resistance to thermal and oxidative influences. Negative temperature coefficient values (0.141–0.127) indicate thermoplastic properties of the material, whereas positive aging coefficients (0.675–1.219) indicate increased stiffness due to oxidation. Multivariate polynomial regression yielded R2 values ​​of 0.962–0.987. Validation against actual data showed the evolved power law rheological model had very small deviations at all temperatures and aging conditions. The power law significantly increased with increasing temperature, aging, and additive addition. © The Author(s) 2026.