相关论文: Backward variational approach on time scales with …

We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality…

In this work we propose a new and more general approach to the calculus of variations on time scales that allows to obtain, as particular cases, both delta and nabla results. More precisely, we pose the problem of minimizing or maximizing…

We develop the calculus of variations on time scales for a functional that is the composition of a certain scalar function with the delta and nabla integrals of a vector valued field. Euler-Lagrange equations, transversality conditions, and…

We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…

We show how a linear control systems theory for the backward nabla differential operator on an arbitrary time scale can be obtained via Caputo's duality. More precisely, we consider linear control systems with outputs defined with respect…

The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the…

We prove a necessary optimality condition of Euler-Lagrange type for variational problems on time scales involving nabla derivatives of higher-order. The proof is done using a new and more general fundamental lemma of the calculus of…

We prove a necessary optimality condition for isoperimetric problems under nabla-differentiable curves. As a consequence, the recent results of [M.R. Caputo, A unified view of ostensibly disparate isoperimetric variational problems, Appl.…

We prove necessary optimality conditions for problems of the calculus of variations on time scales with a Lagrangian depending on the free end-point.

We introduce a fractional calculus on time scales using the theory of delta (or nabla) dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary time scale are proposed, using the…

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to…

The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with…

We introduce a discrete-time fractional calculus of variations on the time scales $\mathbb{Z}$ and $(h\mathbb{Z})_a$. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of…

We study problems of the calculus of variations and optimal control within the framework of time scales. Specifically, we obtain Euler-Lagrange type equations for both Lagrangians depending on higher order delta derivatives and…

In this note we show how one can obtain results from the nabla calculus from results on the delta calculus and vice versa via a duality argument. We provide applications of the main results to the calculus of variations on time scales.

The calculus of variations on time scales is considered. We propose a new approach to the subject that consists in applying a differentiation tool called the contingent epiderivative. It is shown that the contingent epiderivative applied to…

We prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems of the calculus of variations on time scales. Here the Lagrangian depends on the independent variable, an unknown function and…

We establish necessary optimality conditions for variational problems with a Lagrangian depending on a combined Caputo derivative of variable fractional order. The endpoint of the integral is free, and thus transversality conditions are…

We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla…

The problem of existence of solutions to nabla differential equations and nabla differential inclusions on time scales is considered. Under a special form of the set-valued constraint map, sufficient conditions for the existence of at least…