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Existence of positive solutions of fractional‐order elastic beam equation with a non‐Carathéodory nonlinearity
Author(s) -
Liu Yuji
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3560
Subject(s) - mathematics , mathematical analysis , fixed point theorem , banach space , cone (formal languages) , order (exchange) , nonlinear system , boundary value problem , fractional calculus , function (biology) , space (punctuation) , physics , linguistics , philosophy , finance , algorithm , quantum mechanics , evolutionary biology , economics , biology
In this article, the existence of positive solutions of a boundary value problem for nonlinear singular fractional‐order elastic beam equation is established. Here, f depends on t , x , and x ′; f may be singular at t = 0 and t = 1; and f is a non‐Carathéodory function. The results obtained are based upon fixed‐point theorems in a cone in Banach space. An example is included to illustrate the main results. Copyright © 2015 John Wiley & Sons, Ltd.