Related papers: Composition Functionals in Fractional Calculus of …
We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved.…
In this paper, we address the one-parameter families of the fractional integrals and derivatives defined on a finite interval. First we remind the reader of the known fact that under some reasonable conditions, there exists precisely one…
The least action principle, through its variational formulation, possesses a finalist aspect. It explicitly appears in the fractional calculus framework, where Euler-Lagrange equations obtained so far violate the causality principle. In…
We generalize the fractional Caputo derivative to the fractional derivative ${^CD^{\alpha,\beta}_{\gamma}}$, which is a convex combination of the left Caputo fractional derivative of order $\alpha$ and the right Caputo fractional derivative…
An extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional…
English version of abstract: The dynamic optimization problems treated by the calculus of variations are usually solved with the help of the 2nd order Euler-Lagrange differential equations. These equations are, generally speaking,…
We generalize the fractional Caputo derivative to the fractional derivative ${{^CD}^{\alpha,\beta}_{\gamma}}$, which is a convex combination of the left Caputo fractional derivative of order $\alpha$ and the right Caputo fractional…
Lagrangian formalism is established for differential equations with special functions of mathematical physics as solutions. Formalism is based on either standard or non-standard Lagrangians. This work shows that the procedure of deriving…
In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian $L(x(t)$, where $_a^cD_t^\alpha x(t))$ and $0<\alpha< 1$, such that the following…
Whereas in a coordinate-dependent setting the Euler-Lagrange equations establish necessary conditions for solving variational problems in which both the integrands of functionals and the resulting paths are assumed to be sufficiently…
We derive the Euler-Lagrange equations for minimizers of causal variational principles in the non-compact setting with constraints, possibly prescribing symmetries. Considering first variations, we show that the minimizing measure is…
There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the…
We study two generalizations of fractional variational problems by considering higher-order derivatives and a state time delay. We prove a higher-order integration by parts formula involving a Caputo fractional derivative of variable order…
In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This…
We develop a calculus of variations for functionals which are defined on a set of non differentiable curves. We first extend the classical differential calculus in a quantum calculus, which allows us to define a complex operator, called the…
The paper is devoted to the study of the unconditional extremal problem for a fractional linear integral functional defined on a set of probability distributions. In contrast to results proved earlier, the integrands of the integral…
Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to solve the system of fractional…
We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical…
Generalisations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…