Applications of Homogenous Balance Principles Combined with Fractional Calculus Approach and Separate Variable Method on Investigating Exact Solutions to Multidimensional Fractional Nonlinear PDEs

We investigate the exact solutions of multidimensional time-fractional nonlinear PDEs (fnPDEs) in this paper. In terms of the fractional calculus properties and the separate variable method, we present a new homogenous balance principle (HBP) on the basis of the (1 + 1)-dimensional time fnPDEs. Taking advantage of the new types of HBP together with fractional calculus formulas that subtly avoid the chain rule, the fnPDEs can be reduced to spatial PDEs, and then we solve these PDEs by the fractional calculus method and the separate variable approach. In this way, some new type exact solutions of the certain time-fractional (2 + 1)-dimensional KP equation, (3 + 1)-dimensional Zakharov–Kuznetsov (ZK) equation, and Jimbo–Miwa (JM) equation are explicitly obtained under both Riemann–Liouville derivatives and Caputo derivatives. The dynamical analysis of solutions is shown by numerical simulations of taking property parameters as well.