"On a Fractional Oscillator Equation with Natural Boundary Conditions" by Assia Guezane-Lakoud, Rabah Khaldi et al.

Progress in Fractional Differentiation & Applications

Article Title

On a Fractional Oscillator Equation with Natural Boundary Conditions

Authors

Assia Guezane-Lakoud, Laboratory of Advanced Materials, Department of Mathematics, Badji Mokhtar–Annaba University, P.O. Box 12, 23000 Annaba, AlgeriaFollow
Rabah Khaldi
Delﬁm F. M. Torres

Author Country (or Countries)

Algeria

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.

Suggested Reviewers

N/A

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/030302

Recommended Citation

Guezane-Lakoud, Assia; Khaldi, Rabah; and F. M. Torres, Delﬁm (2017) "On a Fractional Oscillator Equation with Natural Boundary Conditions," Progress in Fractional Differentiation & Applications: Vol. 3: Iss. 3, Article 2.
DOI: http://dx.doi.org/10.18576/pfda/030302
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol3/iss3/2

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