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A new scheme for the solution of the nonlinear Caputo–Hadamard fractional differential equations

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Název: A new scheme for the solution of the nonlinear Caputo–Hadamard fractional differential equations
Autoři: Umer Saeed, Mujeeb ur Rehman
Zdroj: Alexandria Engineering Journal, Vol 105, Iss, Pp 56-69 (2024)
Informace o vydavateli: Elsevier BV, 2024.
Rok vydání: 2024
Témata: Operational matrix of differentiation, Caputo–Hadamard fractional differential equations, Operational matrix of integration, Error analysis, Generalized Legendre wavelets, TA1-2040, 0101 mathematics, Adomian polynomials, Engineering (General). Civil engineering (General), 01 natural sciences
Popis: This paper introduces a numerical approach by generalizing Legendre wavelets for solving nonlinear Caputo–Hadamard fractional differential equations. The methodology involves the extension of classical Legendre wavelets, namely the generalized Legendre wavelets (gLWs), along with the development of operational matrices for Hadamard fractional integration and Caputo–Hadamard fractional differentiation. The proposed method combines the gLWs with the Adomian decomposition method to address the nonlinearities inherent in fractional equations through Adomian polynomials. A detailed methodology is presented for applying the proposed method to nonlinear Caputo–Hadamard fractional differential equations, accompanied by error analysis and numerical simulations to demonstrate its reliability and accuracy.
Druh dokumentu: Article
Jazyk: English
ISSN: 1110-0168
DOI: 10.1016/j.aej.2024.06.050
Přístupová URL adresa: https://doaj.org/article/10c38c0aebdc4a96929eec8d8e36d714
Rights: CC BY
Přístupové číslo: edsair.doi.dedup.....cf0395e089d2038d00efa71b274b8293
Databáze: OpenAIRE
Popis
Abstrakt:This paper introduces a numerical approach by generalizing Legendre wavelets for solving nonlinear Caputo–Hadamard fractional differential equations. The methodology involves the extension of classical Legendre wavelets, namely the generalized Legendre wavelets (gLWs), along with the development of operational matrices for Hadamard fractional integration and Caputo–Hadamard fractional differentiation. The proposed method combines the gLWs with the Adomian decomposition method to address the nonlinearities inherent in fractional equations through Adomian polynomials. A detailed methodology is presented for applying the proposed method to nonlinear Caputo–Hadamard fractional differential equations, accompanied by error analysis and numerical simulations to demonstrate its reliability and accuracy.
ISSN:11100168
DOI:10.1016/j.aej.2024.06.050