Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations

Abstract

In this paper, we study the existence of positive solutions for a class of coupled integral boundary value problems of nonlinear semipositone Hadamard fractional differential equationswhere λ, µ, ν are three parameters with 0 < µ < β and 0 < ν < α, α, β ∈ (n − 1, n] are two real numbers and n ≥ 3, D α , D β are the Hadamard fractional derivative of fractional order, and f, g are sign-changing continuous functions and may be singular at t = 1 or/and t = e. First of all, we obtain the corresponding Green's function for the boundary value problem and some of its properties. Furthermore, by means of the nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorems, we derive an interval of λ such that the semipositone boundary value problem has one or multiple positive solutions for any λ lying in this interval. At last, several illustrative examples were given to illustrate the main results. c 2015 All rights reserved.

Positive solutions for a class of nonlinear Hadamard fractional differential equations with a parameter

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Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions

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Existence and viability for fractional differential equations with initial conditions at inner points

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