On numerical approximation of the Riesz–Caputo operator with the fixed/short memory length

In this paper, the Riesz–Caputo operator is studied. This type of fractional operator is a combination of the left and right Caputo derivatives. The series representation of the analyzed fractional operators with fixed memory length is presented. In the main part of the paper, three modified methods...

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Main Authors:	Tomasz Blaszczyk, Krzysztof Bekus, Krzysztof Szajek, Wojciech Sumelka
Format:	Article
Language:	English
Published:	Elsevier 2021-01-01
Series:	Journal of King Saud University: Science
Subjects:	Fractional derivatives Numerical schemes Caputo operator Riesz–Caputo operator Fixed memory length
Online Access:	http://www.sciencedirect.com/science/article/pii/S1018364720303244

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spelling	doaj-a9007eecf47c4ab5ac45a784eb15b4652020-12-31T04:40:59ZengElsevierJournal of King Saud University: Science1018-36472021-01-01331101220On numerical approximation of the Riesz–Caputo operator with the fixed/short memory lengthTomasz Blaszczyk0Krzysztof Bekus1Krzysztof Szajek2Wojciech Sumelka3Czestochowa University of Technology, Department of Mathematics, al. Armii Krajowej 21, 42-200 Czestochowa, Poland; Corresponding author.Czestochowa University of Technology, Department of Mathematics, al. Armii Krajowej 21, 42-200 Czestochowa, PolandPoznan University of Technology, Institute of Structural Analysis, Piotrowo 5 street, 60-965 Poznan, PolandPoznan University of Technology, Institute of Structural Analysis, Piotrowo 5 street, 60-965 Poznan, PolandIn this paper, the Riesz–Caputo operator is studied. This type of fractional operator is a combination of the left and right Caputo derivatives. The series representation of the analyzed fractional operators with fixed memory length is presented. In the main part of the paper, three modified methods of numerical integration are applied for the approximation of the left and right Caputo, and Riesz–Caputo derivatives. Numerical schemes based on three types of interpolating functions (constant, linear and quadratic function) are presented. The in-depth numerical analysis of the presented schemes is conducted. Absolute errors and experimental rates of convergence, for the considered methods, are calculated and presented.http://www.sciencedirect.com/science/article/pii/S1018364720303244Fractional derivativesNumerical schemesCaputo operatorRiesz–Caputo operatorFixed memory length
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Tomasz Blaszczyk Krzysztof Bekus Krzysztof Szajek Wojciech Sumelka
spellingShingle	Tomasz Blaszczyk Krzysztof Bekus Krzysztof Szajek Wojciech Sumelka On numerical approximation of the Riesz–Caputo operator with the fixed/short memory length Journal of King Saud University: Science Fractional derivatives Numerical schemes Caputo operator Riesz–Caputo operator Fixed memory length
author_facet	Tomasz Blaszczyk Krzysztof Bekus Krzysztof Szajek Wojciech Sumelka
author_sort	Tomasz Blaszczyk
title	On numerical approximation of the Riesz–Caputo operator with the fixed/short memory length
title_short	On numerical approximation of the Riesz–Caputo operator with the fixed/short memory length
title_full	On numerical approximation of the Riesz–Caputo operator with the fixed/short memory length
title_fullStr	On numerical approximation of the Riesz–Caputo operator with the fixed/short memory length
title_full_unstemmed	On numerical approximation of the Riesz–Caputo operator with the fixed/short memory length
title_sort	on numerical approximation of the riesz–caputo operator with the fixed/short memory length
publisher	Elsevier
series	Journal of King Saud University: Science
issn	1018-3647
publishDate	2021-01-01
description	In this paper, the Riesz–Caputo operator is studied. This type of fractional operator is a combination of the left and right Caputo derivatives. The series representation of the analyzed fractional operators with fixed memory length is presented. In the main part of the paper, three modified methods of numerical integration are applied for the approximation of the left and right Caputo, and Riesz–Caputo derivatives. Numerical schemes based on three types of interpolating functions (constant, linear and quadratic function) are presented. The in-depth numerical analysis of the presented schemes is conducted. Absolute errors and experimental rates of convergence, for the considered methods, are calculated and presented.
topic	Fractional derivatives Numerical schemes Caputo operator Riesz–Caputo operator Fixed memory length
url	http://www.sciencedirect.com/science/article/pii/S1018364720303244
work_keys_str_mv	AT tomaszblaszczyk onnumericalapproximationoftherieszcaputooperatorwiththefixedshortmemorylength AT krzysztofbekus onnumericalapproximationoftherieszcaputooperatorwiththefixedshortmemorylength AT krzysztofszajek onnumericalapproximationoftherieszcaputooperatorwiththefixedshortmemorylength AT wojciechsumelka onnumericalapproximationoftherieszcaputooperatorwiththefixedshortmemorylength
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On numerical approximation of the Riesz–Caputo operator with the fixed/short memory length

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