Positive solutions for boundary-value problems of nonlinear fractional differential equations
Texas State University-San Marcos, Department of Mathematics
In this paper, we consider the existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary-value problem Dα0 + u(t) = ƒ(t, u(t)), 0 < t < 1 u(0) + u′(0) = 0, u(1) + u′(1) = 0 where 1 < α ≤ 2 is a real number, and Dα0+ is the Caputo's fractional derivative, and ƒ : [0, 1] x [0, +∞) → [0, +∞) is continuous. By means of a fixed-point theorem on cones, some existence and multiplicity results of positive solutions are obtained.
Caputo's fractional derivative, Fractional differential equation, Boundary-value problem, Positive solution, Fractional Green's function, Fixed-point theorem
Zhang, S. (2006). Positive solutions for boundary-value problems of nonlinear fractional differential equations. <i>Electronic Journal of Differential Equations, 2006</i>(36), pp. 1-12.