Fractional view of heat-like equations via the Elzaki transform in the settings of the Mittag-Leffler function

In this article, the Elzaki homotopy perturbation transform method (EHPTM) is profusely employed to discover the approximate solutions of fractional-order (FO) heat-like equations. To show this, we first establish the Elzaki transform in the context of the Atangana-Baleanu fractional derivative in the Caputo sense (ABC) and then extend it to heat-like equations. Our suggested approach has been reinforced by convergence and error analysis. The validity of the novel technique is tested with the aid of some illustrative examples. Comparative analysis has been established for both fractional and integer-order solutions. EHPTM is considered to be an appropriate and convenient approach for solving FO time-dependent linear and nonlinear partial differential problems. Plots and tables are being used to reveal the findings. The relatively high validity and reliability of the present approach are also reflected by the comparative solution analysis by means of statistical analysis.