An efficient computational approach for local fractional Poisson equation in fractal media

In this article, we analyze local fractional Poisson equation (LFPE) by employing q-homotopy analysis transform method (q-HATM). The PE describes the potential field due to a given charge with the potential field known, one can then calculate gravitational or electrostatic field in fractal domain. It is an elliptic partial differential equations (PDE) that regularly appear in the modeling of the electromagnetic mechanism. In this work, PE is studied in the local fractional operator sense. To handle the LFPE some illustrative example is discussed. The required results are presented to demonstrate the simple and well-organized nature of q-HATM to handle PDE having fractional derivative in local fractional operator sense. The results derived by the discussed technique reveal that the suggested scheme is easy to employ and computationally very accurate. The graphical representation of solution of LFPE yields interesting and better physical consequences of Poisson equation with local fractional derivative.

Automated summary

This article analyzes the local fractional Poisson equation (LFPE) using the q-homotopy analysis transform method (q-HATM), discussing the nature of the equation and demonstrating the efficiency of the method in handling partial differential equations with fractional derivatives. The results show that the suggested scheme is easy to employ and computationally very accurate, providing better physical consequences of the Poisson equation with local fractional derivative through graphical representation.