On the fractional deformation of a linearly elastic bar
Fractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local character. A new space, the Λ-space corresponding to...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-04-01
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| Series: | Journal of the Mechanical Behavior of Materials |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jmbm-2020-0002 |
| _version_ | 1818692571530002432 |
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| author | Lazopoulos Konstantinos A. Lazopoulos Anastasios K. |
| author_facet | Lazopoulos Konstantinos A. Lazopoulos Anastasios K. |
| author_sort | Lazopoulos Konstantinos A. |
| collection | DOAJ |
| description | Fractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local character. A new space, the Λ-space corresponding to the initial space is proposed, where the derivatives are local. Transferring the results to the initial space through Riemann-Liouville fractional derivatives, the non-local character of the analysis is shown up. Since fractional derivatives have been established, having the mathematical properties of the derivatives, the linearly elastic fractional deformation of an elastic bar is presented. The fractional axial stress along the distributed body force is discussed. Fractional analysis with horizon is also introduced and the deformation of an elastic bar is also presented. |
| first_indexed | 2024-12-17T12:59:54Z |
| format | Article |
| id | doaj.art-1544726fcbd44e78839d48696eecbdde |
| institution | Directory Open Access Journal |
| issn | 0334-8938 2191-0243 |
| language | English |
| last_indexed | 2024-12-17T12:59:54Z |
| publishDate | 2020-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of the Mechanical Behavior of Materials |
| spelling | doaj.art-1544726fcbd44e78839d48696eecbdde2022-12-21T21:47:24ZengDe GruyterJournal of the Mechanical Behavior of Materials0334-89382191-02432020-04-0129191810.1515/jmbm-2020-0002jmbm-2020-0002On the fractional deformation of a linearly elastic barLazopoulos Konstantinos A.0Lazopoulos Anastasios K.114 Theatrou Str., Rafina, 19009GreeceMathematical Sciences Department, Hellenic Army AcademyVari, 16673GreeceFractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local character. A new space, the Λ-space corresponding to the initial space is proposed, where the derivatives are local. Transferring the results to the initial space through Riemann-Liouville fractional derivatives, the non-local character of the analysis is shown up. Since fractional derivatives have been established, having the mathematical properties of the derivatives, the linearly elastic fractional deformation of an elastic bar is presented. The fractional axial stress along the distributed body force is discussed. Fractional analysis with horizon is also introduced and the deformation of an elastic bar is also presented.https://doi.org/10.1515/jmbm-2020-0002λ-fractional derivativeλ-fractional spacefractional stressfractional deformationfractional body forcesfractional strainfractional horizon |
| spellingShingle | Lazopoulos Konstantinos A. Lazopoulos Anastasios K. On the fractional deformation of a linearly elastic bar Journal of the Mechanical Behavior of Materials λ-fractional derivative λ-fractional space fractional stress fractional deformation fractional body forces fractional strain fractional horizon |
| title | On the fractional deformation of a linearly elastic bar |
| title_full | On the fractional deformation of a linearly elastic bar |
| title_fullStr | On the fractional deformation of a linearly elastic bar |
| title_full_unstemmed | On the fractional deformation of a linearly elastic bar |
| title_short | On the fractional deformation of a linearly elastic bar |
| title_sort | on the fractional deformation of a linearly elastic bar |
| topic | λ-fractional derivative λ-fractional space fractional stress fractional deformation fractional body forces fractional strain fractional horizon |
| url | https://doi.org/10.1515/jmbm-2020-0002 |
| work_keys_str_mv | AT lazopouloskonstantinosa onthefractionaldeformationofalinearlyelasticbar AT lazopoulosanastasiosk onthefractionaldeformationofalinearlyelasticbar |