Positive solutions for a class of fractional differential coupled system with integral boundary value conditions

Abstract

This paper investigates the existence of positive solutions for the following high-order nonlinear fractional differential boundary value problem (BVP, for short)where n − 1 < α ≤ n, n ≥ 3, 0 ≤ λ < 2, D α 0 + is the Caputo fractional derivative. By using the monotone method, the theory of fixed point index on cone for differentiable operators and the properties of Green's function, some new uniqueness and existence criteria for the considered fractional BVP are established. As applications, some examples are worked out to demonstrate the main results. c 2016 All rights reserved.Keywords: Fractional differential equations, differentiable operators, fixed point index theorems on cone, integral boundary value conditions. 2010 MSC: 34A08, 34B15, 34B18.

Multiple Positive Solutions for Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions and a Parameter

“…Let = −1 ( ), 1 = −1 ( ), and lim →∞ = 0 . The proof of 0 = 1 follows by arguing as in [14], so we omit the proof. Hence, there exist 0 and 0 such that…”

“…In consequence, many meaningful results in these fields have been obtained. For details, see [4][5][6][7][8][9][10][11][12][13][14] and references therein.…”

Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems

“…A growing number of outstanding progress has been made in the theory of such BVP in the last decades due mainly to their extensive applications in the fields of hydrodynamics, nuclear physics, biomathematics, chemistry, and control theory. For further details, please see References [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] and references therein.…”

Existence of Solutions for a Class of Coupled Fractional Differential Systems with Nonlocal Boundary Conditions

“…In consequence, the integral boundary value problem of fractional differential equations is gaining much importance and attention. See [17][18][19][20][21] and references therein. For instance, in [19], Zhao and Liu studied the following coupled fractional differential systems with integral boundary conditions: …”