This study examines the flow and heat transfer of a finite thin layer of a hybrid nanofluid across an unstable stretching surface with varying thermal conductivity and viscous dissipation effects. A hybrid nanofluid model is considered to comprise two different types of nanoparticles, and , with kerosene oil used as a base fluid. To study the phenomenon of thermal conduction, a modified version of Fourier’s law model is adopted because in the power-law model, the thermal conductivity depends on the velocity gradient. A system of nonlinear ordinary differential equations is obtained by considering the similarity transformations over the obtained rheological system of partial differential equations which is then tackled by a well-known numerical approach, i.e., the bvp4c MATLAB technique. The rheological impacts of the power-law index, solid volume fraction, film thickness, Eckert number, and modified Prandtl number on temperature and velocity fields are graphically discussed and illustrated. In the presence of nanoparticles, the temperature of the working fluid is enhanced and the power-law index has an inverse relation with the velocity of the hybrid nanofluid.

This paper investigates the existence and controllability of second‐order functional differential equations with infinite delay, incorporating random operators. The existence of solutions is established using the Schauder fixed point theorem, ensuring that solutions exist under specified conditions. Additionally, the controllability of the system is analyzed using fixed point theory, demonstrating that the solutions can be controlled under specific criteria. An example is included to illustrate the application of the theoretical results.