Results 31 to 40 of about 1,884 (305)

The Duality Theory of Fractional Calculus and a New Fractional Calculus of Variations Involving Left Operators Only

Mediterranean Journal of Mathematics
Through duality, it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right operators.
Delfim F M Torres, Torres Delfim F M
exaly   +3 more sources

Generalized Multiparameters Fractional Variational Calculus [PDF]

International Journal of Differential Equations, 2012
This paper builds upon our recent paper on generalized fractional variational calculus (FVC). Here, we briefly review some of the fractional derivatives (FDs) that we considered in the past to develop FVC. We first introduce new one parameter generalized fractional derivatives (GFDs) which depend on two functions, and show that many of the one ...
Om P. Agrawal
openalex   +5 more sources

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

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

Fractional calculus of variations

, 2017
O cálculo de ordem não inteira, mais conhecido por cálculo fracionário, consiste numa generalização do cálculo integral e diferencial de ordem inteira. Esta tese é dedicada ao estudo de operadores fracionários com ordem variável e problemas variacionais específicos, envolvendo também operadores de ordem variável.
Dina Tavares
openalex   +2 more sources

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

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

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

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