Element‐free Galerkin method for a fractional‐order boundary value problem

Abstract

AbstractIn this article, we develop a meshfree numerical solver for fractional‐order governing differential equations. More specifically, we develop a mesh‐free interpolation‐based element‐free Galerkin numerical model for the fractional‐order governing differential equations. The proposed fractional element‐free Garlekin (f‐EFG) numerical model is a lighter and more accurate alternative to existing mesh‐based finite element solvers for the fractional‐order governing differential equations. We demonstrate here that the f‐EFG with moving least squares (MLS) interpolants are naturally suitable for the approximation of fractional‐order derivatives in terms of the corresponding nodal values, thereby alleviating several issues with FE solvers for such integro‐differential governing equations. We demonstrate the efficacy of the proposed numerical model for numerical solutions with benchmark problems on the linear and nonlinear elastic response of nonlocal elastic solid modeled via fractional‐order governing differential equations. However, it must be noted that the proposed f‐EFG algorithm can be extended to fractional‐order governing differential equations in diverse applications, including multiscale and multiphysics studies.