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