Multiobjective fractional variational calculus in terms of a combined Caputo derivative

Abstract

The study of fractional variational problems in terms of a combined fractional Caputo derivative is introduced. Necessary optimality conditions of Euler-Lagrange type for the basic, isoperimetric, and Lagrange variational problems are proved, as well as transversality and sufficient optimality conditions. This allows to obtain necessary and sufficient Pareto optimality conditions for multiobjective fractional variational problems.

Submitted 18-Nov-2010; accepted 28-Oct-2011; to Applied Mathematics and Computation (ISSN: 0096-3003). In press, DOI: 10.1016/j.amc.2011.10.075

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Cited by in corpus (7)

• A formulation of the fractional Noether-type theorem for multidimensional Lagrangians
• Towards a combined fractional mechanics and quantization
• Optimality Conditions for Fractional Variational Problems with Dependence on a Combined Caputo Derivative of Variable Order
• Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense
• Constrained fractional variational problems of variable order
• Variational Problems Involving a Caputo-Type Fractional Derivative
• Generalized Fuzzy Euler-Lagrange equations and transversality conditions