An approximate analytical view of physical and biological models in the setting of Caputo operator via Elzaki transform decomposition method

This article offers a well-organized and novel algorithm for solving time-fractional Fornberg–Whitham, Klein–Gordon equation and biological population models occurring from physics and engineering. The Elzaki (E)-transformation and decomposition process are combined in this algorithm. To evaluate the numerical outcomes of fractional-order partial differential equations, the E-transform decomposition method is generated in series form and nonlinearity terms are decayed. To demonstrate the feasibility of the proposed approach, numerical algorithms and examples are illustrated via graphs and tables. Moreover, it is viewed that the solutions of the new methodology are in strong correlation with the exact findings. Numerical simulations were carried out to ensure that the proposed methods are precise, as shown by the exact solutions resolving complex nonlinear problems.