The flow of an electroconductive incompressible ternary hybrid nanofluid with heat conduction in a boundary layer including metallic nanoparticles (NPs) over an extended cylindrical with magnetic induction effects is reported in this research. The ternary hybrid nanofluid has been synthesized with the dispersion of titanium dioxide, cobalt ferrite, and magnesium oxide NPs in the base fluid water. For a range of economical and biological applications, a computational model is designed to augment the mass and energy conveyance rate and promote the performance and efficiency of thermal energy propagation. The model has been written as a system of partial differential equations. Which are simplified to the system of ordinary differential equations through similarity replacements. The computing approach parametric continuation method is used to further process the resultant first order differential equations. The results are validated with the bvp4c package for accuracy and validity. The outcomes are displayed and analyzed through Figures and Tables. It has been observed that the inverse Prandtl magnetic number and a larger magnetic constant reduce the fluid flow and elevate the energy profile. The variation of ternary hybrid NPs significantly boosts the thermophysical features of the base fluid.

We prove an interesting result on convergence of positive solutions to a nonlinear second‐order difference equation of interest to some two‐periodic solutions to the equation, improving a previous result, and leave an open problem. We also present a method for a unified treatment of closely related nonlinear difference equations, which appear from time to time in the literature.

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In this paper, we prove some common fixed point results for four mappings satisfying generalized contractive condition in S-metric space. Our results extend and improve several previous works.