<p>Graphene nanoribbons (GNRs) are promising materials for developing low-dimensional devices. The edge structure and strain engineering have been shown to influence their electrical properties, particularly in carrier transport. While previous investigations have primarily addressed the phonon limited mobility of armchair and zigzag graphene nanoribbons (AGNRs and ZGNRs), recent progress in GNRs have demonstrated that the periodic coved structures at the ZGNRs ribbon edge can significantly enhance the carrier mobility. This work incorporates electron-phonon interactions across the whole phonon modes and conducts comprehensive study in ZGNRs and coved-edge GNRs (Coved-GNRs) to explore the modulation of electron mobility and further extends to the properties of electronic thermal conductivity. This approach allows us to identify the primary phonon mode that impedes electron transport. Our results indicate that tensile strain induces dynamic stability in Coved-GNRs, whereas compressive strain induces dynamic instability. Additionally, Coved-GNRs exhibit higher electron mobility compared to ZGNRs by reducing the electron-acoustic mode scattering rate, which is found to be the dominant factor in electron-phonon (el-ph) scattering. A similar effect is observed when longitudinal tensile strain is applied, while applying transverse tensile strain resulted in the opposite effect. Comprehensive calculations of el-ph interactions also revealed that strain has the same effect on electronic thermal conductivity. These findings clarify the relationship between coved-edge structures, strain engineering, and carrier transport, providing insights for developing strategies to enhance the mobility and electronic thermal conductivity of GNRs.</p>