On a Fractional Oscillator Equation with Natural Boundary Conditions
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Publication:6282646
DOI10.18576/PFDA/030302arXiv1701.08962WikidataQ57650496 ScholiaQ57650496MaRDI QIDQ6282646
Assia Guezane-Lakoud, Delfim F. M. Torres, Rabah Khaldi
Publication date: 31 January 2017
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.
Nonlinear boundary value problems for ordinary differential equations (34B15) Fractional ordinary differential equations (34A08)
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