Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem

Guezane-Lakoud, A.; Zenkoufi, L.

doi:10.4236/am.2012.39149

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…2 College of Electronics and Information, Zhejiang University of Media and Communications, Hangzhou, 310018, China. 3 Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China.…”

Section: Fractional Casementioning

confidence: 99%

Existence of positive solutions for a third-order multipoint boundary value problem and extension to fractional case

Sun

2016

Bound Value Probl

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In this paper, we study a nonlinear third-order multipoint boundary value problem by the monotone iterative method. We then obtain the existence of monotone positive solutions and establish iterative schemes for approximating the solutions. In addition, we extend the considered problem to the Riemann-Liouville-type fractional analogue. Finally, we give a numerical example for demonstrating the efficiency of the theoretical results.

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Section: Fractional Casementioning

confidence: 99%

Existence of positive solutions for a third-order multipoint boundary value problem and extension to fractional case

Sun

2016

Bound Value Probl

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Existence of positive solutions for a fourth-order three-point boundary value problem

Guezane-Lakoud¹,

Zenkoufi

2015

J. Appl. Math. Comput.

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Approximate solution of linear and nonlinear fractional differential equations under m-point local and nonlocal boundary conditions

et al. 2016

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This paper investigates a computational method to find an approximation to the solution of fractional differential equations subject to local and nonlocal m-point boundary conditions. The method that we will employ is a variant of the spectral method which is based on the normalized Bernstein polynomials and its operational matrices. Operational matrices that we will developed in this paper have the ability to convert fractional differential equations together with its nonlocal boundary conditions to a system of easily solvable algebraic equations. Some test problems are presented to illustrate the efficiency, accuracy, and applicability of the proposed method. MSC: 35C11; 65T99

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Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem

Abstract: By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel'skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1):

Cited by 3 publications

References 13 publications

Existence of positive solutions for a third-order multipoint boundary value problem and extension to fractional case

Existence of positive solutions for a third-order multipoint boundary value problem and extension to fractional case

Existence of positive solutions for a fourth-order three-point boundary value problem

Approximate solution of linear and nonlinear fractional differential equations under m-point local and nonlocal boundary conditions

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