The Investigation of the Fractional-View Dynamics of Helmholtz Equations Within Caputo Operator

Abstract

It is eminent that partial differential equations are extensively meaningful in physics, mathematics and engineering. Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system's dynamical behavior. In the present research, mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives. First, the Helmholtz equations are presented in Caputo's fractional derivative. Then Natural transformation, along with the decomposition method, is used to attain the series form solutions of the suggested problems. For justification of the proposed technique, it is applied to several numerical examples. The graphical representation of the solutions shows that the suggested technique is an accurate and effective technique with a high convergence rate than other methods. The less calculation and higher rate of convergence have confirmed the present technique's reliability and applicability to solve partial differential equations and their systems in a fractional framework.

Approximate analytical solution to the Cattaneo heat conduction model with various laser sources

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Fractional Dynamics of Vector-Borne Infection with Sexual Transmission Rate and Vaccination

“…Fractional-order derivatives have grown in popularity in recent years, and they are now frequently employed in modeling real-world events and exploring disease transmission and control [19][20][21][22][23]. In recent years, various investigations with biological models using fractional-order derivatives have been carried out [24][25][26][27].…”

The Analysis of Fractional-Order Kersten–Krasil Shchik Coupled KdV System, via a New Integral Transform

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