Orthonormal Euler wavelets method for time-fractional Cattaneo equation with Caputo-Fabrizio derivative

In this paper, a new orthonormal wavelets based on the orthonormal Euler polynomials (OEPs) is constructed to approximate the numerical solution of time-fractional Cattaneo equation with Caputo-Fabrizio derivative. By applying the Gram-Schmidt orthonormalization process on sets of Euler polynomials...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 2; pp. 2736 - 2762
Main Authors Xu, Xiaoyong, Zhou, Fengying
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
caputo-fabrizio fractional integral
cattaneo equation
convergence analysis
laplace transform
orthonormal euler wavelets
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Summary:In this paper, a new orthonormal wavelets based on the orthonormal Euler polynomials (OEPs) is constructed to approximate the numerical solution of time-fractional Cattaneo equation with Caputo-Fabrizio derivative. By applying the Gram-Schmidt orthonormalization process on sets of Euler polynomials of various degrees, an explicit representation of OEPs is obtained. The convergence analysis and error estimate of the orthonormal Euler wavelets expansion are studied. The exact formula of Caputo-Fabrizio fractional integral of orthonormal Euler wavelets are derived using Laplace transform. The applicability and validity of the proposed method are verified by some numerical examples.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023144