Results 11 to 20 of about 1,463 (256)

Minimization Problems for Functionals Depending on Generalized Proportional Fractional Derivatives

Fractal and Fractional, 2022
In this work we study variational problems, where ordinary derivatives are replaced by a generalized proportional fractional derivative. This fractional operator depends on a fixed parameter, acting as a weight over the state function and its first-order
Ricardo Almeida
doaj   +1 more source

Fractional Damping Through Restricted Calculus of Variations [PDF]

Journal of Nonlinear Science, 2021
Key words and phrases: Continuous/discrete Lagrangian and Hamiltonian modelling, fractional derivatives, fractional dissipative systems, fractional differential equations, variational principles, variational integrators. 30 pages, 7 figures. Constructive comments are welcome!!
Jiménez Alburquerque, Fernando, Ober-Blöbaum, Sina   +1 more
openaire   +4 more sources

Euler–Lagrange-Type Equations for Functionals Involving Fractional Operators and Antiderivatives

Mathematics, 2023
The goal of this paper is to present the necessary and sufficient conditions that every extremizer of a given class of functionals, defined on the set C1[a,b], must satisfy.
Ricardo Almeida
doaj   +1 more source

Optimal State Control of Fractional Order Differential Systems: The Infinite State Approach

Fractal and Fractional, 2021
Optimal control of fractional order systems is a long established domain of fractional calculus. Nevertheless, it relies on equations expressed in terms of pseudo-state variables which raise fundamental questions.
Jean-Claude Trigeassou, Nezha Maamri
doaj   +1 more source

Variational calculus with conformable fractional derivatives [PDF]

IEEE/CAA Journal of Automatica Sinica, 2017
This is a preprint of a paper whose final and definite form will appear in the IEEE/CAA Journal of Automatica Sinica, ISSN 2329-9266.
Matheus J. Lazo, Delfim F. M. Torres
openaire   +3 more sources

Variational Problems Involving a Generalized Fractional Derivative with Dependence on the Mittag–Leffler Function

Fractal and Fractional, 2023
In this paper, we investigate the necessary conditions to optimize a given functional, involving a generalization of the tempered fractional derivative.
Ricardo Almeida
doaj   +1 more source

Fractional variational problems on conformable calculus

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2021
The authors discuss the optimality conditions of the variational problems including conformable fractional derivatives. They obtain the optimality conditions for Öxed end-point variational problems, and for variable end-point variational problems. Then they investigate the isoperimetric problem, and variational problems with holonomic constraints ...
ÖĞREKÇİ, Süleyman, ASLIYÜCE, Serkan   +1 more
openaire   +5 more sources

Modified Mittag-Leffler Functions with Applications in Complex Formulae for Fractional Calculus

Fractal and Fractional, 2020
Mittag-Leffler functions and their variations are a popular topic of study at the present time, mostly due to their applications in fractional calculus and fractional differential equations.
Arran Fernandez, Iftikhar Husain
doaj   +1 more source

Herglotz Variational Problems Involving Distributed-Order Fractional Derivatives with Arbitrary Smooth Kernels

Fractal and Fractional, 2022
In this paper, we consider Herglotz-type variational problems dealing with fractional derivatives of distributed-order with respect to another function.
Fátima Cruz, Ricardo Almeida, Natália Martins   +2 more
doaj   +1 more source

Further Research for Lagrangian Mechanics within Generalized Fractional Operators

Fractal and Fractional, 2023
In this article, the problems of the fractional calculus of variations are discussed based on generalized fractional operators, and the corresponding Lagrange equations are established.
Chuanjing Song
doaj   +1 more source