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Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.56 no.1 Bogotá jan./jun. 2022 Epub 02-Jan-2024
https://doi.org/10.15446/recolma.v56n1.105612
ORIGINAL ARTICLES
A novel iterative method to solve nonlinear wave-like equations of fractional order with variable coefficients
Un nuevo método iterativo para resolver ecuaciones onduladas no lineales de orden fraccionario con coeficientes variables
1 Ferhat Abbas Sétif University
In this work, we suggest a novel iterative method to give approximate solutions of nonlinear wave-like equations of fractional order with variable coefficients. The advantage of the proposed method is the ability to combine two different methods: Shehu transform method and homotopy analysis method, in addition to providing an approximate solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. This method can be called Shehu homotopy analysis method (SHAM). Three different examples are presented to illustrate the preciseness and effectiveness of the proposed method. The numerical results show that the solutions obtained by SHAM are in good agreement with the solutions found in the literature. Furthermore, the results show that this method can be implemented in an easy way and therefore can be used to solve other nonlinear fractional partial differential equations.
Keywords: Nonlinear wave-like equations with variable coefficients; Caputo fractional derivative; Shehu transform; homotopy analysis method; approximate solution
En este trabajo, sugerimos un método iterativo novedoso para dar una solución aproximada de ecuaciones onduladas no lineales de orden fraccionario con coeficientes variables. La ventaja del método propuesto es la capacidad de combinar dos métodos diferentes: el método de transformación de Shehu y el método de análisis de homotopía, además de proporcionar una solución aproximada en forma de una serie convergente con componentes fácilmente computables, que no requieren linealización ni pequeñas perturbaciones. Este método se puede llamar método de análisis de homotopía Shehu (SHAM). Se presentan tres ejemplos diferentes para ilustrar la precisión y eficacia del método propuesto. Los resultados numéricos muestran que las soluciones obtenidas por SHAM están en buen acuerdo con las soluciones encontradas en la literatura. Además, los resultados muestran que este método es fácil de aplicar y, por lo tanto, se puede utilizar para resolver otras ecuaciones diferenciales parciales fraccionarias no lineales.
Palabras clave: Ecuaciones onduladas no lineales con coeficientes variables; derivada fraccional de Caputo; transformada Shehu; método de análisis de homotopía; solución aproximada
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Received: May 27, 2021; Accepted: May 12, 2022
This is an open-access article distributed under the terms of the Creative Commons Attribution License
