Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order | Zendy

J. Caballero | Zendy; J. Harjani | Zendy; Kishin Sadarangani | Zendy

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Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order

Author(s) -

J. Caballero,

J. Harjani,

Kishin Sadarangani

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/165641

Subject(s) - mathematics , uniqueness , fractional calculus , fixed point theorem , order (exchange) , boundary value problem , mathematical analysis , value (mathematics) , nonlinear system , pure mathematics , derivative (finance) , picard–lindelöf theorem , statistics , physics , finance , quantum mechanics , financial economics , economics

We are concerned with the existence and uniqueness of positive solutions for the following nonlinear fractional boundary value problem: Da(0+)(alpha) u(t) + f(t, u(t)) = 0, 0 <= t 1, 3 < alpha <= 4, u(0) = u'(0) =u(n)(0) = u(n)(1) = 0, where Da(0+)(alpha) denotes the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also given to illustrate the results.

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