Some new exact solutions for nonlinear sequential fractional partial differential equations using the invariant subspace method

Abstract The invariant subspace method is applied for the first time to get exact solutions of nonlinear sequential fractional partial differential equations (FPDEs). We illustrate how this method reduces a nonlinear sequential FPDE to a system of nonlinear sequential ordinary fractional differential equations (FDEs) in the coefficients of the solution expansion. This system is solved using the properties of the fractional derivative of the power function and/or the Laplace transform. We applied this technique to derive exact solutions to some types of sequential fractional Boussinesq equations formulated in both the Riemann–Liouville and Caputo derivative senses. These fractional Boussinesq equations are proposed here for the first time. Therefore, all exact solutions derived in this study for the models under consideration are entirely new.