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Summary Applications of Wavelet Multiresolution Analysis

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Fractional derivatives, unlike those of natural order, have “memory” and are useful to model systems where the past history is relevant. They are defined by means of integral operators, some of them having singular kernels, and calculations may be difficult. It is for that reason that it is necessary to develop numerical approximation methods to solve most of real problems. In this work we combine the wavelet transform with the fractional derivatives of a particular wavelet basis, by means of a Galerkin scheme, to build an approximate solution to boundary value problems involving Caputo-Fabrizio fractional derivatives. The numerical scheme is simple and stable, and its accuracy can be improved as much as desired. We present some numerical examples to show its performance.

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ICIAM 2019 SEMA SIMAI Springer Series 4




Juan Pablo Muszkats
Silvia Alejandra Seminara
María Inés Troparevsky Eds.


Applications
of Wavelet
Multiresolution
Analysis

,SEMA SIMAI Springer Series

ICIAM 2019 SEMA SIMAI Springer Series

Volume 4


Editor-in-Chief
Amadeu Delshams, Departament de Matemàtiques and Laboratory of Geometry and
Dynamical Systems, Universitat Politècnica de Catalunya, Barcelona, Spain

Series Editors
Francesc Arandiga Llaudes, Departamento de Matemàtica Aplicada, Universitat de
València, Valencia, Spain
Macarena Gómez Mármol, Departamento de Ecuaciones Diferenciales y Análisis
Numérico, Universidad de Sevilla, Sevilla, Spain
Francisco M. Guillén-González, Departamento de Ecuaciones Diferenciales y
Análisis Numérico, Universidad de Sevilla, Sevilla, Spain
Francisco Ortegón Gallego, Departamento de Matemáticas, Facultad de Ciencias
del Mar y Ambientales, Universidad de Cádiz, Puerto Real, Spain
Carlos Parés Madroñal, Departamento Análisis Matemático, Estadística e I.O.,
Matemática Aplicada, Universidad de Málaga, Málaga, Spain
Peregrina Quintela, Department of Applied Mathematics, Faculty of Mathematics,
Universidade de Santiago de Compostela, Santiago de Compostela, Spain
Carlos Vázquez-Cendón, Department of Mathematics, Faculty of Informatics,
Universidade da Coruña, A Coruña, Spain
Sebastià Xambó-Descamps, Departament de Matemàtiques, Universitat Politècnica
de Catalunya, Barcelona, Spain

,This sub-series of the SEMA SIMAI Springer Series aims to publish some of the
most relevant results presented at the ICIAM 2019 conference held in Valencia in
July 2019.
The sub-series is managed by an independent Editorial Board, and will include
peer-reviewed content only, including the Invited Speakers volume as well as books
resulting from mini-symposia and collateral workshops.
The series is aimed at providing useful reference material to academic and
researchers at an international level.


More information about this subseries at http://www.springer.com/series/16499

, Juan Pablo Muszkats • Silvia Alejandra Seminara •
María Inés Troparevsky
Editors




Applications of Wavelet
Multiresolution Analysis
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