Analysis of the n-Term Klein-Gordon Equations in Cantor Sets
The effectiveness of the local fractional reduced differential transformation method (LFRDTM) for the approximation of the solution related to the extended n-term local fractional Klein-Gordon equation is the main aim of this paper in which fractional complex transform and local fractional derivativ...
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Akif AKGUL
2023-12-01
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| Series: | Chaos Theory and Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3096978 |
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| author | Nikhil Sharma Sunil Joshi Pranay Goswami |
| author_facet | Nikhil Sharma Sunil Joshi Pranay Goswami |
| author_sort | Nikhil Sharma |
| collection | DOAJ |
| description | The effectiveness of the local fractional reduced differential transformation method (LFRDTM) for the approximation of the solution related to the extended n-term local fractional Klein-Gordon equation is the main aim of this paper in which fractional complex transform and local fractional derivative have been employed to analyze the n-term Klein-Gordon equations, and Cantor sets. The proposed method, along with the existence of the solutions demonstrated through some examples, provides a powerful mathematical means in solving fractional linear differential equations. Considering these points, the paper also provides an accurate and effective method to solve complex physical systems that display fractal or self-similar behavior across various scales. In conclusion, the fractional complex transform with the local fractional differential transform method has been proven to be a robust and flexible approach towards obtaining effective approximate solutions of local fractional partial differential equations. |
| format | Article |
| id | doaj-art-9bcc18656aa8441297823220bd268f7d |
| institution | Kabale University |
| issn | 2687-4539 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj-art-9bcc18656aa8441297823220bd268f7d2025-01-23T18:15:39ZengAkif AKGULChaos Theory and Applications2687-45392023-12-015430831710.51537/chaos.12862941971Analysis of the n-Term Klein-Gordon Equations in Cantor SetsNikhil Sharma0https://orcid.org/0000-0001-8903-2938Sunil Joshi1https://orcid.org/0000-0001-9919-4017Pranay Goswami2https://orcid.org/0000-0003-1205-1975Manipal University JaipurManipal University JaipurDr B. R. Ambedkar UniversityThe effectiveness of the local fractional reduced differential transformation method (LFRDTM) for the approximation of the solution related to the extended n-term local fractional Klein-Gordon equation is the main aim of this paper in which fractional complex transform and local fractional derivative have been employed to analyze the n-term Klein-Gordon equations, and Cantor sets. The proposed method, along with the existence of the solutions demonstrated through some examples, provides a powerful mathematical means in solving fractional linear differential equations. Considering these points, the paper also provides an accurate and effective method to solve complex physical systems that display fractal or self-similar behavior across various scales. In conclusion, the fractional complex transform with the local fractional differential transform method has been proven to be a robust and flexible approach towards obtaining effective approximate solutions of local fractional partial differential equations.https://dergipark.org.tr/en/download/article-file/3096978local fractional calculuslocalfractional differential equations;reduced differential transform methodfractional klein-gordon equation. |
| spellingShingle | Nikhil Sharma Sunil Joshi Pranay Goswami Analysis of the n-Term Klein-Gordon Equations in Cantor Sets Chaos Theory and Applications local fractional calculus localfractional differential equations; reduced differential transform method fractional klein-gordon equation. |
| title | Analysis of the n-Term Klein-Gordon Equations in Cantor Sets |
| title_full | Analysis of the n-Term Klein-Gordon Equations in Cantor Sets |
| title_fullStr | Analysis of the n-Term Klein-Gordon Equations in Cantor Sets |
| title_full_unstemmed | Analysis of the n-Term Klein-Gordon Equations in Cantor Sets |
| title_short | Analysis of the n-Term Klein-Gordon Equations in Cantor Sets |
| title_sort | analysis of the n term klein gordon equations in cantor sets |
| topic | local fractional calculus localfractional differential equations; reduced differential transform method fractional klein-gordon equation. |
| url | https://dergipark.org.tr/en/download/article-file/3096978 |
| work_keys_str_mv | AT nikhilsharma analysisofthentermkleingordonequationsincantorsets AT suniljoshi analysisofthentermkleingordonequationsincantorsets AT pranaygoswami analysisofthentermkleingordonequationsincantorsets |