Green's Theorem for Generalized Fractional Derivatives

Abstract

We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case when the generalized operators are reduced to the standard partial fractional derivatives and fractional integrals in the sense of Riemann-Liouville or Caputo.

This is a preprint of a paper whose final and definite form will appear at http://www.springerlink.com: Fract. Calc. Appl. Anal. 16 (2013), no. 1, in press. Submitted 09-July-2012; accepted, after a revision, 24-Oct-2012

References in corpus (5)

• Fractional Vector Calculus and Fractional Maxwell's Equations
• Fractional embedding of differential operators and Lagrangian systems
• A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String
• Generalized fractional calculus with applications to the calculus of variations
• Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

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• Variable Order Fractional Variational Calculus for Double Integrals
• Generalized fractional operators for nonstandard Lagrangians
• An integral Relationship for a new Fractional One-phase Stefan Problem
• An approximation formula for the Katugampola integral