Existence of positive solutions of fractional‐order elastic beam equation with a non‐Carathéodory nonlinearity | Zendy

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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.

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