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Abstract
Based on properties of Green’s function and by Avery–Peterson fixed point theorem, the existence of multiple positive solutions are obtained for singular p-Laplacian fractional differential equation with infinite-point boundary conditions, and an example is given to demonstrate the validity of our main results.
Highlights
The integer-order system is unstable for a ∈ (0, 1), the fractional dynamic system is stable as 0 < a 1−α
Fractional-order systems have been shown to be more accurate and realistic than integer-order models, and it provides an excellent tool to describe the hereditary properties of material and processes, in viscoelasticity, electrochemistry, porous media, and so on
There has been a significant development in the study of fractional differential equations in recent years, readers can refer to [2, 4,5,6,7,8,9,10, 15,16,17, 21,22,23,24]
Summary
The authors obtained the existence and uniqueness of solutions by using the fixed point theorem for mixed monotone operators. In [20], the author considered following fractional differential equation: D0α+u(t) + g(t)f t, u(t) = 0, 0 < t < 1, with infinite-point boundary condition u(0) = u (0) = · · · = u(n−2)(0) = 0, u(i)(1) = αju(ξj), j=1 where n − 1 < α < n, n 3, i ∈ [1, n − 2] is a fixed integer, αj 0, 0 < ξ1 < ξ2 < · · · < ξj−1 < ξj < · · · < 1 Motivated by the excellent results above, in this paper, the existence of multiple positive solutions are obtained for a singular infinite-point p-Laplacian boundary value problems. Compared with [12], fractional derivative is involved in the nonlinear terms for BVP (1), (2), and multiple positive solutions are obtained for the BVP (1), (2)
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