Invariant subspace method for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e33817" altimg="si4.svg"><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional non-linear time-fractional partial differential equations

In this paper, we generalize the theory of invariant subspace method to ( m + 1 ) -dimensional non-linear time-fractional partial differential equations for first time. More specifically, applicability and efficacy have been systematically investigated through 3 generalized diffusion–convection-wave equation along with appropriate initial conditions. This systematic investigation provides an important technique finding a large class various types subspaces different dimensions above-mentioned equation. Additionally, shown that obtained help derive variety exact solutions can be expressed as combinations exponential, trigonometric, polynomial well-known Mittag-Leffler functions. • We study )-dimensional nonlinear fractional PDEs. Invariant diffusion-convection-wave are derived. Exact derived given in terms function.