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The science of strategy (game theory) is known as the optimal decision-making of autonomous and challenging players in a strategic background. There are different strategies to complete the optimal decision. One of these strategies is the similarity technique. Similarity technique is a generalization of the symmetric strategy, which depends only on the other approaches employed, which can be formulated by altering diversities. One of these methods is the fractal theory. In this investigation, we present a new method studying the similarity analytic solution (SAS) of a 3D-fractal nanofluid system (FNFS). The dynamic evolution is completely given by the concept of differential subordination and majorization. Subordination and majorization relationships are the sets of observable individualities. Game theory can simplify the conditions under which particular sets combine. We offer an explicit construction for the complex possible velocity, energy and thermal functions of two-dimensional fluid flow (the complex variable is suggested in the open unit disk, where the disk is selected at a constant temperature and concentration with uniform velocity). We establish that whenever the 3D-fractal nanofluid system is approximated by a fractal function, the solution has the same property, so a class of fractal tangent function gives SAS. Finally, we demonstrate some simulations and examples that give the consequences of this methodology.

Similarity Analytic Solutions of a 3D-Fractal Nanofluid Uncoupled System Optimized by a Fractal Symmetric Tangent Function