Advanced Methods in the Fractional Calculus of Variations

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

doi:10.1007/978-3-319-14756-7

Cited by 157 publications

(136 citation statements)

References 17 publications

Supporting

Mentioning

136

Contrasting

Order By: Relevance

“…He got the appropriate fractional Euler-Lagrange equations, linking conservative and nonconservative cases. These fractional Euler-Lagrange equations are then used to investigate many physical problems [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Numerical Study for Fractional Euler-Lagrange Equations of a Harmonic Oscillator on a Moving Platform

et al. 2016

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Numerical Study for Fractional Euler-Lagrange Equations of a Harmonic Oscillator on a Moving Platform

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Several works have been published on the calculus of the variations where the fractional derivatives are taken in the sense of Caputo [42,43], Riesz-Caputo [44], and combined Caputo [45]. Malinowska et al [46] discussed advanced methods in the fractional calculus of variations.…”

Section: Introductionmentioning

confidence: 99%

Discrete-Time Fractional Optimal Control

Chiranjeevi

Biswas

2017

Mathematics

View full text Add to dashboard Cite

Abstract:A formulation and solution of the discrete-time fractional optimal control problem in terms of the Caputo fractional derivative is presented in this paper. The performance index (PI) is considered in a quadratic form. The necessary and transversality conditions are obtained using a Hamiltonian approach. Both the free and fixed final state cases have been considered. Numerical examples are taken up and their solution technique is presented. Results are produced for different values of α.

show abstract

“…They are well studied from the theoretical point of view (we refer the reader to books [1][2][3] and articles [4][5][6][7][8][9]). Furthermore, one can find several papers devoted to applications of these types of equations in various fields of science: anomalous diffusion [8,10,11], fractional continuum mechanics [12,13], fractional oscillators [14,15] etc.…”

Section: Introductionmentioning

confidence: 99%

Selected Topics in Contemporary Mathematical Modeling

Grzybowski¹

2017

View full text Add to dashboard Cite

Abstract. In this paper we study the fractional differential equation, containing both the left and right fractional derivatives, with respect to various types of boundary conditions. We transform the fractional differential equation into equivalent integral form. Next, we develop a discrete form of the composition of the left and right fractional integrals, based on the trapezoidal rule of integration, and we obtain a numerical scheme for a fractional integral equation. The discrete form of integral equation is rewritten in the matrix form. Finally, several examples of computations are presented.

show abstract

Advanced Methods in the Fractional Calculus of Variations

Abstract: SpringerBriefs in Applied Sciences and TechnologyMore information about this series at

Cited by 157 publications

References 17 publications

Numerical Study for Fractional Euler-Lagrange Equations of a Harmonic Oscillator on a Moving Platform

Numerical Study for Fractional Euler-Lagrange Equations of a Harmonic Oscillator on a Moving Platform

Discrete-Time Fractional Optimal Control

Selected Topics in Contemporary Mathematical Modeling

Contact Info

Product

Resources

About