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Fractional variations for dynamical systems: Hamilton and Lagrange approaches. (English) Zbl 1122.70013

Summary: Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives.

MSC:

70H30 Other variational principles in mechanics
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
49J05 Existence theories for free problems in one independent variable
70H03 Lagrange’s equations
70H05 Hamilton’s equations
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