# Existence of solutions to nonlinear p-Laplacian fractional differential equations with higher-order derivative terms

 dc.contributor.author Su, You-Hui dc.contributor.author Yun, Yongzhen dc.contributor.author Wang, Dongdong dc.contributor.author Hu, Weimin dc.date.accessioned 2022-02-02T18:47:16Z dc.date.available 2022-02-02T18:47:16Z dc.date.issued 2018-05-07 dc.description.abstract In this article, we discuss the existence of positive solution to a nonlinear p-Laplacian fractional differential equation whose nonlinearity contains a higher-order derivative Dβ0+φp (Dα0+u(t)) + ƒ (t, u(t), u′(t),…, u(n-2)(t)) = 0, t ∈ (0, 1), u(0) = u′(0) = ⋯ = u(n-2)(0) = 0, u(n-2)(1) = αu(n-2)(ξ) = 0, Dα0+ u(0) = Dα0+ u(1) = 0, where n - 1 < α ≤ n, n ≥ 2, 1 < β ≤ 2, 0 < ξ < 1, 0 ≤ α ≤ 1 and 0 ≤ αξα-n ≤ 1, φp(s) = |s|p-2s, p > 1, φ-1p = φq, 1/p + 1/q = 1. Dα0+, Dβ0+ are the standard Riemann-Liouville fractional derivatives, and ƒ ∈ C((0, 1) x [0, +∞)n-1, [0, +∞)). The Green's function of the fractional differential equation mentioned above and its relevant properties are presented, and some novel results on the existence of positive solution are established by using the mixed monotone fixed point theorem and the upper and lower solution method. The interesting of this paper is that the nonlinearity involves the higher-order derivative, and also, two examples are given in this paper to illustrate our main results from the perspective of application. dc.description.department Mathematics dc.format Text dc.format.extent 24 pages dc.format.medium 1 file (.pdf) dc.identifier.citation Su, Y. H., Yun, Y., Wang, D., & Hu, W. (2018). Existence of solutions to nonlinear p-Laplacian fractional differential equations with higher-order derivative terms. Electronic Journal of Differential Equations, 2018(105), pp. 1-24. dc.identifier.issn 1072-6691 dc.identifier.uri https://hdl.handle.net/10877/15272 dc.language.iso en dc.publisher Texas State University, Department of Mathematics dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.source Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. dc.subject Fractional differential equation dc.subject Green's function dc.subject p-Laplacian operator dc.subject Upper and lower solution method dc.title Existence of solutions to nonlinear p-Laplacian fractional differential equations with higher-order derivative terms dc.type Article

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