Adiabatic invariants for disturbed fractional Hamiltonian system in terms of Herglotz differential variational principle
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DOI: 10.1007/s00707-020-02796-3
Abstract: Based on the differential variational principle of Herglotz type, we reveal the internal relation between the perturbation and the adiabatic invariants for fractional Hamiltonian system with combined Caputo derivatives. First, based on the Herglotz variational… read more here.
Keywords: system; variational principle; adiabatic invariants; fractional hamiltonian ... See more keywords
Infinitely many solutions for a class of fractional Hamiltonian systems with combined nonlinearities
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DOI: 10.1007/s13324-017-0197-1
Abstract: This paper concerns the existence of infinitely many solutions for the following fractional Hamiltonian systems: $$\begin{aligned} \left\{ \begin{array}{lllll} -_{t}D^{\alpha }_{\infty }(_{-\infty }D^{\alpha }_{t}x(t))-L(t).x(t)+\nabla W(t,x(t))=0,\\ x\in H^{\alpha }({\mathbb R}, {\mathbb R}^{N}), \end{array} \right. \end{aligned}$$-tD∞α(-∞Dtαx(t))-L(t).x(t)+∇W(t,x(t))=0,x∈Hα(R,RN),where $$\alpha \in… read more here.
Keywords: alpha; infinitely many; hamiltonian systems; fractional hamiltonian ... See more keywords