Two New Approximations for Variable-Order Fractional Derivatives

Two New Approximations for Variable-Order Fractional Derivatives

We introduced a parameter σ(t) which was related to α(t); then two numerical schemes for variable-order Caputo fractional derivatives were derived; the second-order numerical approximation to variable-order fractional derivatives α(t)∈(0,1) and 3-α(t)-order approximation for α(t)∈(1,2) are establish...

Full description

Bibliographic Details
Main Authors: Ruilian Du, Zongqi Liang
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2017/1586249
id doaj-2a362fec55d145a6b607e24d46a7eb0e
record_format Article
spelling doaj-2a362fec55d145a6b607e24d46a7eb0e2020-11-24T20:51:02ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/15862491586249Two New Approximations for Variable-Order Fractional DerivativesRuilian Du0Zongqi Liang1School of Sciences, Jimei University, Xiamen, Fujian 361021, ChinaSchool of Sciences, Jimei University, Xiamen, Fujian 361021, ChinaWe introduced a parameter σ(t) which was related to α(t); then two numerical schemes for variable-order Caputo fractional derivatives were derived; the second-order numerical approximation to variable-order fractional derivatives α(t)∈(0,1) and 3-α(t)-order approximation for α(t)∈(1,2) are established. For the given parameter σ(t), the error estimations of formulas were proven, which were higher than some recently derived schemes. Finally, some numerical examples with exact solutions were studied to demonstrate the theoretical analysis and verify the efficiency of the proposed methods.http://dx.doi.org/10.1155/2017/1586249
collection DOAJ
language English
format Article
sources DOAJ
author Ruilian Du
Zongqi Liang
spellingShingle Ruilian Du
Zongqi Liang
Two New Approximations for Variable-Order Fractional Derivatives
Discrete Dynamics in Nature and Society
author_facet Ruilian Du
Zongqi Liang
author_sort Ruilian Du
title Two New Approximations for Variable-Order Fractional Derivatives
title_short Two New Approximations for Variable-Order Fractional Derivatives
title_full Two New Approximations for Variable-Order Fractional Derivatives
title_fullStr Two New Approximations for Variable-Order Fractional Derivatives
title_full_unstemmed Two New Approximations for Variable-Order Fractional Derivatives
title_sort two new approximations for variable-order fractional derivatives
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2017-01-01
description We introduced a parameter σ(t) which was related to α(t); then two numerical schemes for variable-order Caputo fractional derivatives were derived; the second-order numerical approximation to variable-order fractional derivatives α(t)∈(0,1) and 3-α(t)-order approximation for α(t)∈(1,2) are established. For the given parameter σ(t), the error estimations of formulas were proven, which were higher than some recently derived schemes. Finally, some numerical examples with exact solutions were studied to demonstrate the theoretical analysis and verify the efficiency of the proposed methods.
url http://dx.doi.org/10.1155/2017/1586249
work_keys_str_mv AT ruiliandu twonewapproximationsforvariableorderfractionalderivatives
AT zongqiliang twonewapproximationsforvariableorderfractionalderivatives
_version_ 1716802980057972736

Similar Items