Abstract
In this paper, we study the boundary value problem of a Riemann-Liouville fractional q-difference equation. By applying the Leggett-Williams fixed point theorem and the properties of the Green’s function, three positive solutions are obtained.
Highlights
In this paper, we study the boundary value problem of a Riemann-Liouville fractional q-difference equation
Inspired by papers (Kang et al, 2019), (Zhao, Sun, Han, & Li, 2011), (Zhang, 2016) and (Tariboon & Ntouyas, 2014), we study the following nonlinear boundary value problem for a fractional q-differential equation:(t) + f (t, x(t)) = 0, 0 < q < 1, t ∈ (a, b), a ≥ 0, 2 < α < 3, x(a) =(a) =(b) = 0, (1.3) (1.4)
From Lemma 3.1, we know that x(t) is a solution of boundary value problem (1.3)-(1.4) if and only if it satisfies b x(t) = G(t, qs + (1 − q)a) f (s, x(s))adq s, t ∈ [a, b]
Summary
Abstract In this paper, we study the boundary value problem of a Riemann-Liouville fractional q-difference equation. By applying the Leggett-Williams fixed point theorem and the properties of the Green’s function, three positive solutions are obtained.
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