Explicit solutions for fractional Chaffee–Infante reaction–diffusion coupled hierarchy system with conservation laws

This research investigates the explicit series solutions of the fractional Chaffee–Infante reaction–diffusion coupled hierarchy system utilizing Lie symmetry analysis in two-dimensional space. This fractional system is a prominent model in fluid dynamics to characterize the surface-stripe wave evolution of liquids in light of the theory of conservation laws. The governing fractional system is analytically solved by the well-defined technique, called the power series method, so that the total derivative used is based on the Riemann–Liouville derivative. Simulations are also provided in this direction. The acquired results are systematically validated through a series of test cases. The results show that the proposed method is robust, accurate, and flexible in gaining more solutions, and it is effective in treating various fractional physical phenomena within the framework of conservation laws as well.