EQUIVALENT POWER-FORM TRANSFORMATION FOR FRACTAL BRATU’S EQUATION

ELà AS-ZÚÑIGA Alex, Luis Manuel Palacios-Pineda (), Isaac H. Jimã‰nez-Cedeã‘o (), Oscar Martã Nez-Romero () and Daniel Olvera Trejo ()
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ELà AS-ZÚÑIGA Alex: Department of Mechanical Engineering and Advanced Materials, School of Engineering and Science, Tecnologico de Monterrey, Av. E. Garza Sada 2501 Sur, Monterrey, Nuevo León, 64849, México
Luis Manuel Palacios-Pineda: ��Tecnológico Nacional de México, Instituto Tecnológico de Pachuca, Carretera México - Pachuca Km. 87.5, C.P. 42080, Colonia Venta Prieta, Pachuca de Soto, Hgo., Mexico
Isaac H. Jimã‰nez-Cedeã‘o: ��Engineering Department, Safran Mexico Av. Ishikawa # 1001, (Esquina con Av. Taguchi) Parque Industrial Supra, C.P. 31183, Chihuahua, Ch., Mexico
Oscar Martã Nez-Romero: Department of Mechanical Engineering and Advanced Materials, School of Engineering and Science, Tecnologico de Monterrey, Av. E. Garza Sada 2501 Sur, Monterrey, Nuevo León, 64849, México
Daniel Olvera Trejo: Department of Mechanical Engineering and Advanced Materials, School of Engineering and Science, Tecnologico de Monterrey, Av. E. Garza Sada 2501 Sur, Monterrey, Nuevo León, 64849, México

FRACTALS (fractals), 2021, vol. 29, issue 01, 1-8

Abstract: In this paper, an equivalent power-form transformation method with a weighted function is applied for solving the one-dimensional fractal Bratu’s boundary value equation. Numerical integration solutions obtained from the equivalent Bratu’s equation as well as those from its approximate Taylor’s series solution reveal that the proposed methodology yields highly accurate solutions. Therefore, it is believed that by applying the power-form transformation, various fractal differential equations in which two scales are needed because of the physical laws involved in modeling the observed phenomena, can be solved by treating the nonlinear terms as equivalent power-form terms.

Keywords: Taylor Series; Fractal Bratu’s Equation; Two-Scale Transform; Equivalent Power-Form Weighted Approach (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:01:n:s0218348x21500195

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DOI: 10.1142/S0218348X21500195

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