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High-dimensional fractional equations research is a cutting-edge field with significant practical and theoretical implications in mathematics, physics, biological fluid mechanics, and other fields. Firstly, in this paper, the (4 + 1)-dimensional time-fractional Fokas equation in a higher-dimensional integrable system is studied by using semi-inverse and fractional variational theory. Then, the Lie symmetry analysis and conservation law analysis are carried out for the higher dimensional fractional order model with the symmetry of fractional order. Finally, the fractional-order equation is solved using the bilinear approach to produce the rogue wave and multi-soliton solutions, and the fractional equation is numerically solved using the Radial Basis Functions (RBFs) method.

Analysis of Lie Symmetries with Conservation Laws and Solutions of Generalized (4 + 1)-Dimensional Time-Fractional Fokas Equation