On existence and uniqueness of positive solutions to a class of fractional boundary value problems

Abstract

The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem

On the existence of solutions of fractional integro-differential equations

“…In [5]- [7], Balachandran et al proved the existence of solutions of integro-differential equations in Banach spaces. Also, we can find existence results for boundary value problems of fractional differential equations in the survey by Agarwal et al [2] and in the papers [1], [10], [14], and [32]. In [11], Clément et al proved the existence of Hölder continuous solutions for a partial fractional differential equation and in [18], Kilbas et al studied the existence of solutions of several classes of ordinary fractional differential equations.…”

Positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator

“…For some recent contributions on fractional differential equations, see for example, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and the references therein. Especially, in [15], by means of Guo-Krasnosel'skiĭ's fixed point theorem, Zhao et al investigated the existence of positive solutions for the nonlinear fractional boundary value problem (BVP for short) In [16], relying on the Krasnosel'skiĭ's fixed point theorem as well as on the LeggettWilliams fixed point theorem, Kaufmann and Mboumi discussed the existence of positive solutions for the following fractional BVP D α 0+ u(t) + a(t)f (u(t)) = 0, 0 < t < 1, 1 < α ≤ 2, u(0) = 0, u (1) = 0.…”