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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/1586249 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549493867806720 |
|---|---|
| author | Ruilian Du Zongqi Liang |
| author_facet | Ruilian Du Zongqi Liang |
| author_sort | Ruilian Du |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-2a362fec55d145a6b607e24d46a7eb0e |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-2a362fec55d145a6b607e24d46a7eb0e2025-02-03T06:11:12ZengWileyDiscrete 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 |
| spellingShingle | Ruilian Du Zongqi Liang Two New Approximations for Variable-Order Fractional Derivatives Discrete Dynamics in Nature and Society |
| title | 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_short | Two New Approximations for Variable-Order Fractional Derivatives |
| title_sort | two new approximations for variable order fractional derivatives |
| url | http://dx.doi.org/10.1155/2017/1586249 |
| work_keys_str_mv | AT ruiliandu twonewapproximationsforvariableorderfractionalderivatives AT zongqiliang twonewapproximationsforvariableorderfractionalderivatives |