Investigation of the Time Fractional Higher-Dimensional Nonlinear Modified Equation of Wave Propagation

Abstract

In this article, we analyzed the time fractional higher-dimensional nonlinear modified model of wave propagation, namely the (3 + 1)-dimensional Benjamin–Bona–Mahony-type equation. The fractional sense was defined by the classical Riemann–Liouville fractional derivative. We derived firstly the existence of symmetry of the time fractional higher-dimensional equation. Next, we constructed the one-dimensional optimal system to the time fractional higher-dimensional nonlinear modified model of wave propagation. Subsequently, it was reduced into the lower-dimensional fractional differential equation. Meanwhile, on the basis of the reduced equation, we obtained its similarity solution. Through a series of analyses of the time fractional high-dimensional model and the results of the above obtained, we can gain a further understanding of its essence.