Conformable finite element method for conformable fractional partial differential equations

Abstract

<abstract><p>The finite element (FE) method is a widely used numerical technique for approximating solutions to various problems in different fields such as thermal diffusion, mechanics of continuous media, electromagnetism and multi-physics problems. Recently, there has been growing interest among researchers in the application of fractional derivatives. In this paper, we present a generalization of the FE method known as the conformable finite element method, which is specifically designed to solve conformable fractional partial differential equations (CF-PDE). We introduce the basis functions that are used to approximate the solution of CF-PDE and provide error estimation techniques. Furthermore, we provide an illustrative example to demonstrate the effectiveness of the proposed method. This work serves as a starting point for tackling more complex problems involving fractional derivatives.</p></abstract>