Exact solutions and maximal dimension of invariant subspaces of time fractional coupled nonlinear partial differential equations

• We demonstrate, first time, how the invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations(PDEs).
• We explain how invariant subspace method provides an effective tool to derive exact solution of time fractional coupled nonlinear PDEs.
• The time fractional coupled nonlinear PDEs admit more than one invariant subspaces which can be explicitly illustrated.
• We explicitly derive more than one exact solution for a given time fractional coupled nonlinear PDEs using invariant subspace method.
• We consider four new times fractional coupled nonlinear PDEs and derive their exact solution. In some examples the exact solution can be expressed in terms of the well known Mittag-Leffler function.

We show how invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations and construct their exact solutions. Effectiveness of the method has been illustrated through time fractional Hunter–Saxton equation, time fractional coupled nonlinear diffusion system, time fractional coupled Boussinesq equation and time fractional Whitman–Broer–Kaup system. Also we explain how maximal dimension of the time fractional coupled nonlinear partial differential equations can be estimated.