Abstract :
In this paper, we investigate the multiple and infinitely solvability of positive solutions for nonlinear
fractional differential equation Du(t) = tνf (u), 0 < t <1, where D = t−βδD
γ−δ,δ
β , β >0,
γ 0, 0 < δ <1, ν >−β(γ + 1). Our main work is to deal with limit case of f (s)/s as s →0 or
s→∞and Φ(s)/s, Ψ(s)/s as s →0 or s→∞, where Φ(s), Ψ(s) are functions connected with
function f . In J.Math. Appl. 252 (2000) 804–812, we consider the existence of a positive solution for
the particular case of Eq. (1.1), i.e., the Riemann–Liouville type (β = 1, γ = 0) nonlinear fractional
differential equation, using the super-lower solutions method. Here, we devote to the existence of
positive solution and multi-positive solutions for Eq. (1.1) by means of the fixed point theorems for
the cone.
2003 Elsevier Science (USA). All rights reserved
