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Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
Ricardo Almeida, Delfim F. M. Torres
We prove optimality conditions for different variational functionals containing left and right Caputo fractional derivatives. A sufficient condition of minimization under an approp…
Generalized Euler-Lagrange equations for variational problems with scale derivatives
Ricardo Almeida, Delfim F. M. Torres
We obtain several Euler-Lagrange equations for variational functionals defined on a set of Hölder curves. The cases when the Lagrangian contains multiple scale derivatives, depends…
Leitmann's direct method for fractional optimization problems
Ricardo Almeida, Delfim F. M. Torres
Based on a method introduced by Leitmann [Internat. J. Non-Linear Mech. {\bf 2} (1967), 55--59], we exhibit exact solutions for some fractional optimization problems of the calculu…
A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String
Ricardo Almeida, Agnieszka B. Malinowska, Delfim F. M. Torres
We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integral…