Fractional calculus of variations for a combined Caputo derivative

By Agnieszka B. Malinowska, Delfim F. M. Torres. 2011

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We generalize the fractional Caputo derivative to the fractional derivative CDγα,β, 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 CDγα,β. The Euler-Lagrange equations for the basic and isoperimetric problems, as well as transversality conditions, are proved.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

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