Abstract
We investigate a singular fractional differential equation with an infinite-point fractional boundary condition, where the nonlinearity f(t,x) may be singular at x = 0, and g(t) may also have singularities at t= 0 or t=1. We establish the existence of positive solutions using the fixed point index theory in cones.
Highlights
1 Introduction We consider the existence of positive solutions for the following fractional nonlocal boundary value problem:
We investigate the existence of positive solutions for the singular fractional infinite-point boundary value problems (BVPs) (1.1) using the fixed point index theory in cones
A has at least one fixed point x∗ ∈ Kr4 \K r1, which is a positive solution of BVP (1.1)
Summary
We consider the existence of positive solutions for the following fractional nonlocal boundary value problem:. The existence of positive solutions for fractional differential equation multipoint boundary value problems (BVPs) have been studied by many authors; see [24,25,26,27,28,29,30,31,32,33]. We investigate the existence of positive solutions for the singular fractional infinite-point BVP (1.1) using the fixed point index theory in cones. Lemma 2.5 ([38]) Let K be a cone in a Banach space E, and let T : Kr → K be a completely continuous operator. Suppose that φ1 is the positive eigenfunction corresponding to λ1 and that A has no fixed points on ∂Kr1. A has at least one fixed point x∗ ∈ Kr4 \K r1 , which is a positive solution of BVP (1.1)
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