Generalized Multiparameters Fractional Variational Calculus
This paper builds upon our recent paper on generalized fractional variational calculus (FVC). Here, we briefly review some of the fractional derivatives (FDs) that we considered in the past to develop FVC. We first introduce new one parameter generalized fractional derivatives (GFDs) which depend on...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2012/521750 |
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| _version_ | 1832558157941964800 |
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| author | Om Prakash Agrawal |
| author_facet | Om Prakash Agrawal |
| author_sort | Om Prakash Agrawal |
| collection | DOAJ |
| description | This paper builds upon our recent paper on generalized fractional variational calculus (FVC). Here, we briefly review some of the fractional derivatives (FDs) that we considered in the past to develop FVC. We first introduce new one parameter generalized fractional derivatives (GFDs) which depend on two functions, and show that many of the one-parameter FDs considered in the past are special cases of the proposed GFDs. We develop several parts of FVC in terms of one parameter GFDs. We point out how many other parts could be developed using the properties of the one-parameter GFDs. Subsequently, we introduce two new two- and three-parameter GFDs. We introduce some of their properties, and discuss how they can be used to develop FVC. In addition, we indicate how these formulations could be used in various fields, and how the generalizations presented here can be further extended. |
| format | Article |
| id | doaj-art-211d01cf733845e89ac5271ce143e039 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-211d01cf733845e89ac5271ce143e0392025-02-03T01:33:04ZengWileyInternational Journal of Differential Equations1687-96431687-96512012-01-01201210.1155/2012/521750521750Generalized Multiparameters Fractional Variational CalculusOm Prakash Agrawal0Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, IL 62901, USAThis paper builds upon our recent paper on generalized fractional variational calculus (FVC). Here, we briefly review some of the fractional derivatives (FDs) that we considered in the past to develop FVC. We first introduce new one parameter generalized fractional derivatives (GFDs) which depend on two functions, and show that many of the one-parameter FDs considered in the past are special cases of the proposed GFDs. We develop several parts of FVC in terms of one parameter GFDs. We point out how many other parts could be developed using the properties of the one-parameter GFDs. Subsequently, we introduce two new two- and three-parameter GFDs. We introduce some of their properties, and discuss how they can be used to develop FVC. In addition, we indicate how these formulations could be used in various fields, and how the generalizations presented here can be further extended.http://dx.doi.org/10.1155/2012/521750 |
| spellingShingle | Om Prakash Agrawal Generalized Multiparameters Fractional Variational Calculus International Journal of Differential Equations |
| title | Generalized Multiparameters Fractional Variational Calculus |
| title_full | Generalized Multiparameters Fractional Variational Calculus |
| title_fullStr | Generalized Multiparameters Fractional Variational Calculus |
| title_full_unstemmed | Generalized Multiparameters Fractional Variational Calculus |
| title_short | Generalized Multiparameters Fractional Variational Calculus |
| title_sort | generalized multiparameters fractional variational calculus |
| url | http://dx.doi.org/10.1155/2012/521750 |
| work_keys_str_mv | AT omprakashagrawal generalizedmultiparametersfractionalvariationalcalculus |