Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques

Abstract

In this article, three different techniques, the Fractional Perturbation Iteration Method (FPIA), Fractional Successive Differentiation Method (FSDM), and Fractional Novel Analytical Method (FNAM), have been introduced. These three iterative methods are applied on different types of Electrical RLC-Circuit Equations of fractional-order. The fractional series approximation of the derived solutions can be established by using the obtained coefficients. These three algorithms handle the problems in a direct manner without any need for restrictive assumptions. The comparison displays an agreement between the obtained results. The beauty of this paper lies in the error analysis between the exact solution and approximate solutions obtained by these three methods which prove that the Approximate Solution obtained by FNAM converge very rapidly to the exact solution.

Keywords

• Fractional Novel Analytical Method
• Fractional Perturbation Iteration Method
• Fractional Successive Differentiation Method
• caputo fractional operator
• fractional-order electrical RLC-circuit equations