This research paper investigates the thermal examination of a non-integer-ordered mobile fin situation with a hybrid nanofluid flowing past it at an unceasing speed U. The combination approach is utilized to evaluate the physical and thermal characteristics of the hybrid nanofluid, excluding the thermal conductivity and dynamic viscosity. This governing equation is transformed into a dimensionless form and the Adomian Decomposition Sumudu Transform method is employed to solve the conundrum of a moving fin immersed in a hybrid nanofluid. The reliability of this research has been confirmed by verifying the results through a comparison with numerical simulations. The influence of diverse factors on the thermal overview for varying noninteger values alpha is analyzed and presented in graphical representations. Moreover, the analysis reveals that the highest heat flux occurs in the scenario where nanoparticles with spherical-platelet shapes are combined. This is succeeded by the spherical-cylindrical combination, and finally, the spherical-spherical pairing, in terms of heat flux magnitude. Here, we discovered that the temperature at the fin tip decreases by 11.19141 % for s-s shaped nanoparticles, 10.45649 % for s-c shaped nanoparticles and 10.21162 % for s-p shaped nanoparticles as the wet parameter (m2) increases by a factor of 400, and also when the radiation parameter is increased by 400 %, the temperature of the fin tip drops by 13.11313 % for s-s shape nanoparticles, 11.97076 for s-c shape nanoparticles and 11.653899 % for s-p shape nanoparticles.