On a New Measure on Fractals
| dc.contributor.author | Baleanu, Dumitru | |
| dc.contributor.author | Golmankhaneh, Alireza K. | |
| dc.date.accessioned | 2022-10-06T12:09:21Z | |
| dc.date.accessioned | 2025-09-18T12:08:22Z | |
| dc.date.available | 2022-10-06T12:09:21Z | |
| dc.date.available | 2025-09-18T12:08:22Z | |
| dc.date.issued | 2013 | |
| dc.description | Khalili Golmankhaneh, Alireza/0000-0002-5008-0163 | en_US |
| dc.description.abstract | Fractals are sets whose Hausdorff dimension strictly exceeds their topological dimension. The algorithmic Riemannian-like method, F-alpha-calculus, has been suggested very recently. Henstock-Kurzweil integral is the generalized Riemann integral method by using the gauge function. In this paper we generalize the F-alpha-calculus as a fractional local calculus that is more suitable to describe some physical process. We introduce the new measure using the gauge function on fractal sets that gives a finer dimension in comparison with the Hausdorff and box dimension. Hilbert F-alpha-spaces are defined. We suggest the self-adjoint F-alpha-differential operator so that it can be applied in the fractal quantum mechanics and on the fractal curves. | en_US |
| dc.identifier.citation | Golmankhaneh, Alireza K.; Baleanu, Dumitru (2013). "On a new measure on fractals", Journal of Inequalities and Applications, Vol. 2013. | en_US |
| dc.identifier.doi | 10.1186/1029-242X-2013-522 | |
| dc.identifier.issn | 1029-242X | |
| dc.identifier.scopus | 2-s2.0-84897584668 | |
| dc.identifier.uri | https://doi.org/10.1186/1029-242X-2013-522 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12416/11115 | |
| dc.language.iso | en | en_US |
| dc.publisher | Springer | en_US |
| dc.relation.ispartof | Journal of Inequalities and Applications | |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Fractal Measure | en_US |
| dc.subject | Fractal Calculus | en_US |
| dc.subject | Fractal Curve | en_US |
| dc.title | On a New Measure on Fractals | en_US |
| dc.title | On a new measure on fractals | tr_TR |
| dc.type | Article | en_US |
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| gdc.author.id | Khalili Golmankhaneh, Alireza/0000-0002-5008-0163 | |
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| gdc.author.wosid | Golmankhaneh, Alireza/L-1534-2013 | |
| gdc.author.wosid | Baleanu, Dumitru/B-9936-2012 | |
| gdc.author.wosid | Khalili Golmankhaneh, Alireza/L-1554-2013 | |
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| gdc.description.department | Çankaya University | en_US |
| gdc.description.departmenttemp | [Golmankhaneh, Alireza K.] Islamic Azad Univ, Dept Phys, Urmia Branch, Orumiyeh 969, Iran; [Baleanu, Dumitru] King Abdulaziz Univ, Fac Engn, Dept Chem & Mat Engn, POB 80204, Jeddah 21589, Saudi Arabia; [Baleanu, Dumitru] Cankaya Univ, Dept Math & Comp Sci, TR-06530 Ankara, Turkey; [Baleanu, Dumitru] Inst Space Sci, Magurele 76900, Romania | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
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| gdc.oaire.keywords | Applied Mathematics | |
| gdc.oaire.keywords | Discrete Mathematics and Combinatorics | |
| gdc.oaire.keywords | Analysis | |
| gdc.oaire.keywords | fractal curve | |
| gdc.oaire.keywords | Fractals | |
| gdc.oaire.keywords | fractal calculus | |
| gdc.oaire.keywords | fractal measure | |
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