Generalized Multiparameters Fractional Variational Calculus

Om Prakash Agrawal

International Journal of Differential Equations, 2012, vol. 2012, 1-38

Abstract:

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.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJDE/2012/521750.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJDE/2012/521750.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:521750

DOI: 10.1155/2012/521750

Access Statistics for this article

More articles in International Journal of Differential Equations from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().