Variational methods for the fractional Sturm–Liouville problem

Abstract

This article is devoted to the regular fractional Sturm-Liouville eigenvalue problem. Applying methods of fractional variational analysis we prove existence of countable set of orthogonal solutions and corresponding eigenvalues. Moreover, we formulate two results showing that the lowest eigenvalue is the minimum value for a certain variational functional.

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

“…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].…”

Conclusion

“…The results mentioned in this book were first published in peer reviewed international journals (Bourdin et al 2013(Bourdin et al , 2014Klimek et al 2014;Odzijewicz et al 2012aOdzijewicz et al , b, c, 2013bOdzijewicz andTorres 2012, 2014); chapters in books (Odzijewicz 2013b;Odzijewicz et al 2013a); and proceedings with referee (Odzijewicz et al 2010(Odzijewicz et al , 2012d. See also the PhD thesis (Odzijewicz 2013a).…”

A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems

“…In [18]- [20], [21], extended some spectral properties of fractional Sturm-Liouville problem. Variational Methods and Inverse Laplace transform method applied in [23] and [24], respectively. In [25], it is presented a series method for solving higher eigenvalue Sturm-Liouville problems.…”