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Entropy 2014, 16(1), 471-493; doi:10.3390/e16010471
Article

Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

1
, 1
, 2
 and 3,4,*
Received: 10 November 2013; in revised form: 11 December 2013 / Accepted: 11 December 2013 / Published: 9 January 2014
(This article belongs to the Special Issue Dynamical Systems)
View Full-Text   |   Download PDF [402 KB, updated 15 January 2014; original version uploaded 9 January 2014]
Abstract: The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.
Keywords: multiple solutions; fractional differential equations; power series multiple solutions; fractional differential equations; power series
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Arqub, O.A.; El-Ajou, A.; Al Zhour, Z.; Momani, S. Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique. Entropy 2014, 16, 471-493.

AMA Style

Arqub OA, El-Ajou A, Al Zhour Z, Momani S. Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique. Entropy. 2014; 16(1):471-493.

Chicago/Turabian Style

Arqub, Omar A.; El-Ajou, Ahmad; Al Zhour, Zeyad; Momani, Shaher. 2014. "Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique." Entropy 16, no. 1: 471-493.


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