Open Access
Translator Disclaimer
2012 Generalized Multiparameters Fractional Variational Calculus
Om Prakash Agrawal
Int. J. Differ. Equ. 2012(SI2): 1-38 (2012). DOI: 10.1155/2012/521750


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.


Download Citation

Om Prakash Agrawal. "Generalized Multiparameters Fractional Variational Calculus." Int. J. Differ. Equ. 2012 (SI2) 1 - 38, 2012.


Received: 2 April 2012; Accepted: 8 August 2012; Published: 2012
First available in Project Euclid: 2 October 2020

zbMATH: 1268.26008
MathSciNet: MR2975375
Digital Object Identifier: 10.1155/2012/521750

Rights: Copyright © 2012 Hindawi


Vol.2012 • No. SI2 • 2012
Back to Top