Fractional calculus of variations for a combined Caputo derivative

Malinowska, Agnieszka B.; Torres, Delfim F. M.

doi:10.2478/s13540-011-0032-6

Cited by 67 publications

(47 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The pioneering work of Riewe has attracted the interest of other scientists; we quote some of them here and refer the reader also to the references therein [1,3,4,5,6,8,9]. While reading some of the (many) papers written in the subject we were led to some questions.…”

Section: Introductionmentioning

confidence: 99%

Fractional Calculus of Variations: A Novel Way to Look At It

Ferreira¹

2019

FCAA

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Fractional Calculus of Variations: A Novel Way to Look At It

Ferreira¹

2019

FCAA

View full text Add to dashboard Cite

show abstract

“…A generalization of traditional calculus of variations for systems that are described by the Riemann-Liouville fractional derivatives has been suggested by Agrawal in [1]. Subsequent by extensions of variational calculus for the Riemann-Liouville derivatives [5] and other type of fractional derivatives such as the Caputo derivative [15,18,19], the Hadamard derivative [3], the Riesz derivatives [2], and fractional integrals [4] have been derived. It should be noted that the extension of variational calculus for the Riesz derivatives, suggested in [2], is really derived for so-called the Riesz-RiemannLiouville and the Riesz-Caputo derivatives rather than the usual Riesz fractional derivatives [23].…”

Section: Introductionmentioning

confidence: 99%

Variational principle of stationary action for fractional nonlocal media and fields

Tarasov

2015

Pac. J. Math. Ind.

View full text Add to dashboard Cite

Derivatives and integrals of non-integer orders have a wide application to describe complex properties of physical systems and media including nonlocality of power-law type and long-term memory. We suggest an extension of the standard variational principle for fractional nonlocal media with power-law type nonlocality that is described by the Riesz-type derivatives of non-integer orders. As examples of application of the suggested variational principle, we consider an N-dimensional model of waves in anisotropic fractional nonlocal media, and a one-dimensional continuum (string) with power-law spatial dispersion. The main advantage of the suggested fractional variational principle is that it is connected with microstructural lattice approach and the lattice fractional calculus, which is recently proposed.

show abstract

“…In the work [29] Green theorem for generalized partial fractional derivatives was proved. Other applications of fractional variational principles are presented in [2,19,25,26,28].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of fractional Sturm-Liouville equation in integral form

Błaszczyk

Ciesielski

2014

fcaa

View full text Add to dashboard Cite

In this paper a fractional differential equation of the Euler-Lagrange/ Sturm-Liouville type is considered. The fractional equation with derivatives of order α ∈ (0, 1] in the finite time interval is transformed to the integral form. Next the numerical scheme is presented. In the final part of this paper examples of numerical solutions of this equation are shown. The convergence of the proposed method on the basis of numerical results is also discussed.MSC 2010 : Primary 26A33; Secondary 34A08, 65L10

show abstract

Fractional calculus of variations for a combined Caputo derivative

Abstract: We generalize the fractional Caputo derivative to the fractional deriv-

Cited by 67 publications

References 52 publications

Fractional Calculus of Variations: A Novel Way to Look At It

Fractional Calculus of Variations: A Novel Way to Look At It

Variational principle of stationary action for fractional nonlocal media and fields

Numerical solution of fractional Sturm-Liouville equation in integral form

Contact Info

Product

Resources

About