Abstract <p>In this article, the analytic solutions of the heat-like (HL) and wave-like (WL) equations in two and three dimensional with time fractional order were successfully obtained using a new fractional analytical iterative approach. The novelty of the study is the use of the Caputo fractional operator to solve nonlinear fractional partial differential equations with more complex solutions and to solve classical equations with incredibly accurate answers from well-known series solutions. It also does not necessitate any presumptions for nonlinear expressions. Numerical results for various equation scenarios are displayed using tables and graphs. For the new technique, the convergence analysis was performed successfully. The technique is very good at minimizing the size of analytical stages while still being easy and fast to solve nonlinear fractional equations.</p>