3,800 research outputs found
On fractional derivatives and primitives of periodic functions
In this paper we prove that the fractional derivative or the fractional
primitive of a -periodic function cannot be a -periodic function,
for any period , with the exception of the zero function.Comment: 12 page
Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection
A human respiratory syncytial virus surveillance system was implemented in
Florida in 1999, to support clinical decision-making for prophylaxis of
premature newborns. Recently, a local periodic SEIRS mathematical model was
proposed in [Stat. Optim. Inf. Comput. 6 (2018), no.1, 139--149] to describe
real data collected by Florida's system. In contrast, here we propose a
non-local fractional (non-integer) order model. A fractional optimal control
problem is then formulated and solved, having treatment as the control.
Finally, a cost-effectiveness analysis is carried out to evaluate the cost and
the effectiveness of proposed control measures during the intervention period,
showing the superiority of obtained results with respect to previous ones.Comment: This is a preprint of a paper whose final and definite form is with
'Chaos, Solitons & Fractals', available from
[http://www.elsevier.com/locate/issn/09600779]. Submitted 23-July-2018;
Revised 14-Oct-2018; Accepted 15-Oct-2018. arXiv admin note: substantial text
overlap with arXiv:1801.0963
Multiplicity and concentration results for some nonlinear Schr\"odinger equations with the fractional -Laplacian
We consider a class of parametric Schr\"odinger equations driven by the
fractional -Laplacian operator and involving continuous positive potentials
and nonlinearities with subcritical or critical growth. By using variational
methods and Ljusternik-Schnirelmann theory, we study the existence,
multiplicity and concentration of positive solutions for small values of the
parameter
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