Numerical simulation of fractional-order two-dimensional Helmholtz equations

Abstract

In this paper, we investigate the exact solutions of several fractional-order Helmholtz equations using the homotopy perturbation transform method. We specify sufficient requirements for its convergence and provide error estimations. The homotopy perturbation transform method yields a quickly converging succession of solutions. Solutions for various fractional space derivatives are compared to present approaches and explained using figures. Appropriate parameter selection produces approximations identical to the exact answer. Test examples are provided to demonstrate the proposed approach's precision and competence. The results demonstrate that our system is appealing, user-friendly, dependable, and highly effective.

Keywords

• fractional helmholtz equations
• caputo operator
• homotopy perturbation transform method
• analytical solution