Fractional variational problems depending on indefinite integrals. (English) Zbl 1236.49042

Almeida, Ricardo; Pooseh, Shakoor; Torres, Delfim F. M.

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 3, 1009-1025 (2012).

Summary: We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main results give fractional Euler–Lagrange type equations and natural boundary conditions, which provide a generalization of the previous results found in the literature. Isoperimetric problems, problems with holonomic constraints and depending on higher-order Caputo derivatives, as well as fractional Lagrange problems, are considered.

MSC:

49K05	Optimality conditions for free problems in one independent variable
49S05	Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
26A33	Fractional derivatives and integrals
34A08	Fractional ordinary differential equations and fractional differential inclusions

Keywords:

calculus of variations; fractional calculus; Caputo derivatives; fractional necessary optimality conditions

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