Results 261 to 270 of about 1,774 (281)

Fractional Calculus of Variations and the Brachistochrone Problem

SSRN Electronic Journal, 2018
The Brachistochrone problem was posed by Johann Bernoulli as a challenge in 1697. It is still an appropriate problem as an example for application in many branches of mathematics. The problem was first solved by Newton in 1697 itself. Later this problem was solved by using Euler-Lagrange equation with the Calculus of Variations.
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Fractional Calculus of Variations in Dynamics

2010
In mathematics and theoretical physics, variational (functional) derivative is a generalization of usual derivative that arises in the calculus of variations. In a variation instead of differentiating a function with respect to a variable, one differentiates a functional with respect to a function.
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Fractional variational calculus and the transversality conditions

Journal of Physics A: Mathematical and General, 2006
This paper presents the Euler–Lagrange equations and the transversality conditions for fractional variational problems. The fractional derivatives are defined in the sense of Riemann–Liouville and Caputo. The connection between the transversality conditions and the natural boundary conditions necessary to solve a fractional differential equation is ...
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Standard Methods in Fractional Variational Calculus

2015
We investigate the problem of finding an admissible function giving a minimum value to an integral functional that depends on an unknown function (or functions) of one or several variables and its generalized fractional derivatives and/or generalized fractional integrals.
Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F. M. Torres   +2 more
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Fractional calculus of variations

2018
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.
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Direct Methods in Fractional Calculus of Variations

2015
In this chapter, under assumptions of regularity, convexity and coercivity, we obtain sufficient conditions ensuring the existence of minimizers for functionals with a Lagrangian depending on generalized fractional derivatives and integrals. Necessary optimality conditions of Euler–Lagrange type are also given.
Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F. M. Torres   +2 more
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Fractional variational calculus in terms of Riesz fractional derivatives

Journal of Physics A: Mathematical and Theoretical, 2007
This paper presents extensions of traditional calculus of variations for systems containing Riesz fractional derivatives (RFDs). Specifically, we present generalized Euler–Lagrange equations and the transversality conditions for fractional variational problems (FVPs) defined in terms of RFDs.
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Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations

Journal of Geometric Mechanics, 2022
Jacky Cresson, Fernando Jiménez, Sina Ober-Blöbaum   +2 more
exaly  

Calculus of variations on time scales and discrete fractional calculus

2011
Estudamos problemas do cálculo das variações e controlo óptimo no contexto das escalas temporais. Especificamente, obtemos condições necessárias de optimalidade do tipo de Euler–Lagrange tanto para lagrangianos dependendo de derivadas delta de ordem superior como para problemas isoperimétricos.
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A formulation of Noether's theorem for fractional problems of the calculus of variations

Journal of Mathematical Analysis and Applications, 2007
Gastao S F Frederico, Delfim F M Torres
exaly