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Fractional calculus of variations for a combined Caputo derivative

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Abstract

We generalize the fractional Caputo derivative to the fractional derivative C D α,β γ , which is a convex combination of the left Caputo fractional derivative of order α and the right Caputo fractional derivative of order β. The fractional variational problems under our consideration are formulated in terms of C D α,β. γ The Euler-Lagrange equations for the basic and isoperimetric problems, as well as transversality conditions, are proved.

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Authors and Affiliations

  1. Faculty of Computer Science, Białystok University of Technology, 15-351, Białystok, Poland

    Agnieszka B. Malinowska

  2. Center for Research and Development in Mathematics and Applications Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Delfim F. M. Torres

Authors
  1. Agnieszka B. Malinowska
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  2. Delfim F. M. Torres
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Corresponding author

Correspondence to Agnieszka B. Malinowska.

Additional information

This work was presented in part at the IFAC Workshop on Fractional Derivatives and Applications (IFAC FDA’2010), held in University of Extremadura, Badajoz, Spain, October 18–20, 2010.

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Malinowska, A.B., Torres, D.F.M. Fractional calculus of variations for a combined Caputo derivative. fcaa 14, 523–537 (2011). https://doi.org/10.2478/s13540-011-0032-6

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