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Non Probabilistic Solution of Fuzzy Fractional Fornberg-Whitham Equation

S. Chakraverty1,2, Smita Tapaswini1
Department of Mathematics, National Institute of Technology Rourkela Odisha – 769 008, India.Tel: +91661-2462713; Fax: +91661-2462713-2701
Corresponding Author. E-mail: sne_chak@yahoo.com

Computer Modeling in Engineering & Sciences 2014, 103(2), 71-90. https://doi.org/10.3970/cmes.2014.103.071

Abstract

Fractional Fornberg-Whitham equation has a vast application in physics. There exist various investigations for the above problem by considering the variables and parameters as crisp/exact. In practice, we may not have these parameters exactly but those may be known in some uncertain form. In the present paper, these uncertainties are taken as interval/fuzzy and the authors proposed here a new method viz. that of the double parametric form of fuzzy numbers to handle the uncertain fractional Fornberg-Whitham equation. Using the single parametric form of fuzzy numbers, original fuzzy fractional Fornberg-Whitham equation is converted first to an interval based fuzzy differential equation. Next this equation is transformed to crisp form by applying the proposed double parametric form of fuzzy numbers. Finally it has been solved using homotopy perturbation method (HPM). Present method performs very well in terms of computational efficiency. The reliability of the method is shown by obtaining an approximate numerical solution for different cases. Results are given in term of plots and are also compared in special cases.

Keywords

Triangular fuzzy number, Gaussian fuzzy number, r-cut, Double parametric form of fuzzy number, fuzzy fractional Fornberg-Whitham equation, HPM

Cite This Article

Chakraverty, S., Tapaswini, S. (2014). Non Probabilistic Solution of Fuzzy Fractional Fornberg-Whitham Equation. CMES-Computer Modeling in Engineering & Sciences, 103(2), 71–90.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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