The study presents an analytical investigation on enhancing thermal conductivity using spherical graphene and strontium titanate nanoparticles in a carboxymethyl cellulose base fluid flowing over an accelrated Riga plate. The flow of the hybrid nanofluid is modeled using the Caputo-Fabrizio fractional derivative. The research explores the effects of various parameters, including the fractional derivative order, Lorentz force, and nanoparticle volume fractions, on fluid velocity and temperature profiles. Derivation of analytical solutions to describe the unsteady free convection flow of the hybrid nanofluid were obtained using the Laplace transform method. Key findings suggest that increasing the fractional parameter enhances both fluid velocity and temperature, while changes in the nanoparticle volume fraction and thermal radiation parameter influence fluid behavior in opposite directions, with temperature increasing and velocity decreasing. The study highlights the potential of combining graphene’s high thermal conductivity with strontium titanate’s unique properties to optimize nanofluid performance, especially in electromagnetic environments, and emphasizes the utility of fractional derivatives in modeling complex fluid dynamics.