The solution comparison of fractional Heat transfer and porous media equations using analytical techniques

Abstract In this paper, the mathematical model related to the physical problem of electrostatic or gravitational area in the fractal domain is the Poisson equation, which analyses the potential area arising from a given charge with the possibility of the area identified being considered in fractional form. The Laplace residual power series method and the Laplace Adomian decomposition technique are used to compare the solutions of the fractional local Poisson equation. The phenomenon of electromagnetic mechanisms is typically modelled using elliptic partial differential equations. Furthermore, the Poisson equation is examined using the concept of fractional local derivative. For this reason, a few examples are presented to understand the fractional local Poisson equation in its more accurate form. The results show the simple and sophisticated procedures of the two proposed analytical approaches where partial differential equations are considered with fractional derivatives or local derivatives. The outcomes of the described methods demonstrate that they have an accurate algorithm to construct with exceptionally precise cost calculation capabilities. The present research is more related to the fractional local Poisson equation and also to the fractional local derivative of the Poisson equation, which produces pleasing results.