The thermal radiation effect on Casson nanofluids EG-GO and EG-CNTs models using Caputo fractional order derivative with shape effects: Via analytical investigations

This research examines the analytical investigations for radiating Casson nanofluid models with unsteady convecting flow, which are valued by the order of Caputo fractional derivative (CFD). Ethylene glycol (EG) is used as a base fluid, and graphene oxide (GO) and carbon nanotubes (CNTs) are used as nanoparticles. The problem’s leading PDEs are nondimensionalized by applying the proper nondimensional variables. The solutions to the dimensionless governing equations are found by using the Fourier sine and Laplace transformation techniques together. For an enormous study of the problem, graphical illustrations and tables are developed by using MATLAB software programming with the help of Euler inversion. We examine the impact on the fractional heat and momentum equation of the [Formula: see text], Gr, Pr, [Formula: see text], R, [Formula: see text], oscillations. Using the properties of the fluid, important discoveries were made that indicated a number of elements for a number of flow parameters as well as fractional parameters. The thermal profiles are increased for [Formula: see text] decreased for [Formula: see text] at [Formula: see text] and [Formula: see text]. The velocity profiles are increased for R and Gr decreased for [Formula: see text] and [Formula: see text] at [Formula: see text] and 1.4. Different shapes of nanoparticles are performed for ordinary fractional parameters, which are increased for temperature as well as velocity.