New Derivatives on the Fractal Subset of Real-Line
In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-01-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/18/2/1 |
| _version_ | 1798034143420874752 |
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| author | Alireza Khalili Golmankhaneh Dumitru Baleanu |
| author_facet | Alireza Khalili Golmankhaneh Dumitru Baleanu |
| author_sort | Alireza Khalili Golmankhaneh |
| collection | DOAJ |
| description | In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on the fractals subset of real-line lies in the fact that they are better at modeling processes with memory effect. |
| first_indexed | 2024-04-11T20:40:09Z |
| format | Article |
| id | doaj.art-ceaae02b446546b28342889e86582446 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T20:40:09Z |
| publishDate | 2016-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-ceaae02b446546b28342889e865824462022-12-22T04:04:14ZengMDPI AGEntropy1099-43002016-01-01182110.3390/e18020001e18020001New Derivatives on the Fractal Subset of Real-LineAlireza Khalili Golmankhaneh0Dumitru Baleanu1Department of Physics, College of Science, Urmia Branch, Islamic Azad University, Urmia, IranDepartment of Mathematics and Computer Science, Faculty of Art and Sciences, Cankaya University, Ankara 06530, TurkeyIn this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on the fractals subset of real-line lies in the fact that they are better at modeling processes with memory effect.http://www.mdpi.com/1099-4300/18/2/1fractal calculustriadic Cantor setnon-local Laplace transformationmemory processesgeneralized Mittag-Leffler functiongeneralized gamma functiongeneralized beta function |
| spellingShingle | Alireza Khalili Golmankhaneh Dumitru Baleanu New Derivatives on the Fractal Subset of Real-Line Entropy fractal calculus triadic Cantor set non-local Laplace transformation memory processes generalized Mittag-Leffler function generalized gamma function generalized beta function |
| title | New Derivatives on the Fractal Subset of Real-Line |
| title_full | New Derivatives on the Fractal Subset of Real-Line |
| title_fullStr | New Derivatives on the Fractal Subset of Real-Line |
| title_full_unstemmed | New Derivatives on the Fractal Subset of Real-Line |
| title_short | New Derivatives on the Fractal Subset of Real-Line |
| title_sort | new derivatives on the fractal subset of real line |
| topic | fractal calculus triadic Cantor set non-local Laplace transformation memory processes generalized Mittag-Leffler function generalized gamma function generalized beta function |
| url | http://www.mdpi.com/1099-4300/18/2/1 |
| work_keys_str_mv | AT alirezakhaliligolmankhaneh newderivativesonthefractalsubsetofrealline AT dumitrubaleanu newderivativesonthefractalsubsetofrealline |