Birkhoff equations on time scales and Noether theorem for Birkhoffian system on time scales
are studied. First, some necessary knowledge of calculus on time scales are reviewed …

We prove a time scales version of the Noether theorem relating group of symmetries and
conservation laws in the framework of the shifted and nonshifted Δ calculus of variations …

Several conditions ensuring existence of solutions of a dynamic Sturm–Liouville boundary
value problem are derived. Variational methods are utilized in the proofs. An example …

This paper deals with Noether symmetry and conserved quantities for the Hamiltonian
system of Herglotz type on time scales. Firstly, the variational principle of Herglotz type for …

Full article: Generalized transversality conditions for the Hahn quantum variational calculus
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The time scale calculus theory can be applicable to any field in which dynamic processes
are described by discrete-or continuous-time models. On the other hand, many economic …

We develop Cresson's nondifferentiable calculus of variations on the space of Hölder
functions. Several quantum variational problems are considered: with and without …

In calculus of variations on general time scales, an Euler–Lagrange equation of integral form
is usually derived in order to characterize the critical points of nonshifted Lagrangian …

In this paper, we give conditions guaranteeing the existence of at least three solutions for a
second-order dynamic Sturm–Liouville boundary value problem involving two parameters …

We introduce differential, integral, and variational delta embeddings. We prove that the
integral delta embedding of the Euler–Lagrange equations and the variational delta …