On a Fractional Oscillator Equation with Natural Boundary Conditions
Classical Analysis and ODEs
2017-06-12 v1
Abstract
We prove existence of solutions for a nonlinear fractional oscillator equation with both left Riemann-Liouville and right Caputo fractional derivatives subject to natural boundary conditions. The proof is based on a transformation of the problem into an equivalent lower order fractional boundary value problem followed by the use of an upper and lower solutions method. To succeed with such approach, we first prove a result on the monotonicity of the right Caputo derivative.
Keywords
Cite
@article{arxiv.1701.08962,
title = {On a Fractional Oscillator Equation with Natural Boundary Conditions},
author = {Assia Guezane-Lakoud and Rabah Khaldi and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1701.08962},
year = {2017}
}
Comments
This is a preprint of a paper whose final and definite form is published in Prog. Frac. Diff. Appl. 3 (2017). See [http://dx.doi.org/10.18576/pfda]