Abstract
In this paper, we consider a class of fractional differential equations with infinite-point boundary value conditions. Under some conditions concerning the spectral radius with respect to the relevant linear operator, both the existence of uniqueness and the nonexistence of positive solution are obtained by means of the iterative technique.
Highlights
In this paper, we consider the following fractional differential equations (FDE for short) with infinite-point boundary value conditions:⎧ ⎨Dα0+u(t) + a(t)f (t, u(t)) = 0, 0 < t < 1,⎩u(0) = u (0) = · · · = u(n–2)(0) = 0, Dβ0+u(1) = ∞ i=1 ηiDβ0+u(ξi ), (1.1)where α ≥ 2, n – 1 < α ≤ n, 0 < β < α – 1, ηi ∈ R, 0 < ξ1 < · · · < ξi < ξi+1 < · · · < 1 (i = 1, 2, . . .), ∞ i=1 ηiξiα–β = Dα0+
Liang and Zhang [9] studied the uniqueness of positive solution for the following fractional three-point Boundary value problems (BVP):
Motivated by the above works, in this paper we aim to establish the existence of uniqueness and the nonexistence of positive solution to BVP (1.1)
Summary
We consider the following fractional differential equations (FDE for short) with infinite-point boundary value conditions: In [16], the authors discussed the following fractional m-point BVP: There are few works on the uniqueness of solution for fractional boundary value problems [4, 5, 9, 17, 21, 22, 24, 26].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
