NOTE ON KNEZEVIC-MILJANOVIC'S THEOREM IN A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS

作者：Kawasaki Toshiharu^*; Toyoda Masashi

来源：Journal of Nonlinear and Convex Analysis, 2015, 16(11): 2235-2241.

In this paper, we show the existence and uniqueness of solutions of the Cauchy problem in a class of singular fractional differential equations. Let 1 < alpha <= 2. We consider the Cauchy problem
{D-0(alpha)+u(t) = p(t)(a)u(t)(sigma),
lim(t -> 0+) u(t) = 0 lim(t -> 0) u'(t)/t(alpha-2) = (alpha - 1)lambda
where p is continuous, alpha, sigma, lambda is an element of R with sigma < 0, lambda > 0 and D-0+(alpha) is the RiemannLiouville fractional derivative. If alpha = 2, then this problem is the problem in [6].

• 出版日期2015