An efficient computational approach for local fractional Poisson equation in fractal media. Issue 2 (3rd November 2020)

• Record Type: Journal Article
• Authors: Singh, Jagdev; Ahmadian, Ali; Rathore, Sushila; Kumar, Devendra; Baleanu, Dumitru; Salimi, Mehdi; Salahshour, Soheil
• Is Part Of: Numerical methods for partial differential equations. Volume 37:Issue 2(2021)
• Page Start: 1439
• Page End: 1448
• Publication Date: 2020-11-03
• Subjects: local fractional derivative -- local fractional Laplace transform -- local fractional Poisson equation -- q‐homotopy analysis transform method; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22589
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: 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.