Abstract
In this paper, the existence of a positive solution to a boundary value problem of fractional differential equations with the p-Laplacian operator is studied. By applying a monotone iterative method, some existence results of positive solutions are obtained. In addition, an example is included to illustrate the main results.
Highlights
In this paper, we consider the following boundary value problem of fractional differential equations with a p-Laplacian operator: Dγ φp Dαu(t) = f t, u(t), 0 < t < 1, (1.1)u(0) = Dαu(0) = 0, Dβ u(1) = aDβ u(ξ ), Dαu(1) = bDαu(η), (1.2)where α, β, γ ∈ R; 1 < α, γ ≤ 2; β > 0 and 1 + β ≤ α; ξ, η ∈ (0, 1); a, b ∈ [0, +∞); 1 – aξ α–β–1 > 0; 1 bp–1ηγ –1 and φp(s) =
We study the existence of positive solutions for boundary value problem (1.1), by applying a monotone iterative method, some existence results of positive solutions are obtained
Zhanbing Bai, professor, his main research field is fractional differential equations and boundary value problems
Summary
1 Introduction In this paper, we consider the following boundary value problem of fractional differential equations with a p-Laplacian operator: Dγ φp Dαu(t) = f t, u(t) , 0 < t < 1, (1.1) We study the existence of positive solutions for boundary value problem (1.1), by applying a monotone iterative method, some existence results of positive solutions are obtained. 3, we prove the main results about the existence of positive solution of the boundary value problem (1.1). Definition 2.2 ([32]) The Riemann–Liouville fractional derivative of order α > 0 of a continuous function x : (0, +∞) → R is given by
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