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Volume 16
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Article

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

by
Omar Abu Arqub
1,
Ahmad El-Ajou
1,
Zeyad Al Zhour
2 and
Shaher Momani
3,4,*
1
Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan
2
Department of Basic Sciences and Humanities, College of Engineering, University of Dammam, Dammam 31451, Kingdom of Saudi Arabia
3
Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan
4
Department of Mathematics, Faculty of Science, King AbdulAziz University, Jeddah 21589, Kingdom of Saudi Arabia
*
Author to whom correspondence should be addressed.
Entropy 2014, 16(1), 471-493; https://doi.org/10.3390/e16010471
Submission received: 10 November 2013 / Revised: 11 December 2013 / Accepted: 11 December 2013 / Published: 9 January 2014
(This article belongs to the Special Issue Dynamical Systems)
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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

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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. https://doi.org/10.3390/e16010471

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. https://doi.org/10.3390/e16010471

Chicago/Turabian Style

Arqub, Omar Abu, Ahmad El-Ajou, Zeyad Al Zhour, and Shaher Momani. 2014. "Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique" Entropy 16, no. 1: 471-493. https://doi.org/10.3390/e16010471

APA Style

Arqub, O. A., El-Ajou, A., Al Zhour, Z., & Momani, S. (2014). Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique. Entropy, 16(1), 471-493. https://doi.org/10.3390/e16010471

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