An effective computational approach to the local fractional low-pass electrical transmission lines model
In this research, a new fractional low-pass electrical transmission lines model (LPETLM) described by the local fractional derivative (LFD) is derived for the first time. By defining the Mittag-Leffler function (MLF) on the Cantor set (CS), two special functions, namely, theLTδ-function and LCδ-func...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-01-01
|
| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824007439 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841553813551448064 |
|---|---|
| author | Kang-Jia Wang |
| author_facet | Kang-Jia Wang |
| author_sort | Kang-Jia Wang |
| collection | DOAJ |
| description | In this research, a new fractional low-pass electrical transmission lines model (LPETLM) described by the local fractional derivative (LFD) is derived for the first time. By defining the Mittag-Leffler function (MLF) on the Cantor set (CS), two special functions, namely, theLTδ-function and LCδ-function, are extracted to develop an auxiliary function, which is employed to look for the non-differentiable (ND) exact solutions (ESs) together with Yang’s non-differentiable transformation. Eight sets of the ESs are obtained and the corresponding dynamic performances on the CS for γ=ln2/ln3 are displayed. As expected, for γ→1, the ESs of the local fractional LPETLM become the ESs of the classic LPETLM and the outlines are also depicted graphically. The outcomes confirm that our new method is a promising tool to handle the local fractional PDEs in the electrical and electronic engineering. |
| format | Article |
| id | doaj-art-5687d0c7fe6f445b9070a44fb5825164 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-5687d0c7fe6f445b9070a44fb58251642025-01-09T06:13:15ZengElsevierAlexandria Engineering Journal1110-01682025-01-01110629635An effective computational approach to the local fractional low-pass electrical transmission lines modelKang-Jia Wang0Corresponding author.; School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, ChinaIn this research, a new fractional low-pass electrical transmission lines model (LPETLM) described by the local fractional derivative (LFD) is derived for the first time. By defining the Mittag-Leffler function (MLF) on the Cantor set (CS), two special functions, namely, theLTδ-function and LCδ-function, are extracted to develop an auxiliary function, which is employed to look for the non-differentiable (ND) exact solutions (ESs) together with Yang’s non-differentiable transformation. Eight sets of the ESs are obtained and the corresponding dynamic performances on the CS for γ=ln2/ln3 are displayed. As expected, for γ→1, the ESs of the local fractional LPETLM become the ESs of the classic LPETLM and the outlines are also depicted graphically. The outcomes confirm that our new method is a promising tool to handle the local fractional PDEs in the electrical and electronic engineering.http://www.sciencedirect.com/science/article/pii/S1110016824007439Local fractional derivativeLow-pass electrical transmission lines modelCantor setsMittag-Leffler functionAuxiliary function |
| spellingShingle | Kang-Jia Wang An effective computational approach to the local fractional low-pass electrical transmission lines model Alexandria Engineering Journal Local fractional derivative Low-pass electrical transmission lines model Cantor sets Mittag-Leffler function Auxiliary function |
| title | An effective computational approach to the local fractional low-pass electrical transmission lines model |
| title_full | An effective computational approach to the local fractional low-pass electrical transmission lines model |
| title_fullStr | An effective computational approach to the local fractional low-pass electrical transmission lines model |
| title_full_unstemmed | An effective computational approach to the local fractional low-pass electrical transmission lines model |
| title_short | An effective computational approach to the local fractional low-pass electrical transmission lines model |
| title_sort | effective computational approach to the local fractional low pass electrical transmission lines model |
| topic | Local fractional derivative Low-pass electrical transmission lines model Cantor sets Mittag-Leffler function Auxiliary function |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824007439 |
| work_keys_str_mv | AT kangjiawang aneffectivecomputationalapproachtothelocalfractionallowpasselectricaltransmissionlinesmodel AT kangjiawang effectivecomputationalapproachtothelocalfractionallowpasselectricaltransmissionlinesmodel |