FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 6, PAGES 137-155

**On the number of real eigenvalues of a certain boundary-value
problem for a second-order equation with fractional derivative**

A. Yu. Popov

Abstract

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The asymptotics as $$a → 0+ of the
number of real eigenvalues $$l_{n}(a) of the problem
$y\text{'}\text{'}(x)\; +$lD_{0}^{a}y(x) = 0,
$0\; <\; x\; <\; 1$, $y(0)\; =\; y(1)\; =\; 0$, is found.
The minimization of real eigenvalues was carried out.
It is proved that $lim$_{a → 0+} l_{n}(a) =
(pn)^{2}.

Location: http://mech.math.msu.su/~fpm/eng/k06/k066/k06609h.htm

Last modified: February 26, 2007