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  • Open Access


    Modifications of the Optimal Auxiliary Function Method to Fractional Order Fornberg-Whitham Equations

    Hakeem Ullah1, Mehreen Fiza1,*, Ilyas Khan2,*, Abd Allah A. Mosa3, Saeed Islam1, Abdullah Mohammed4

    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 277-291, 2023, DOI:10.32604/cmes.2023.022289

    Abstract In this paper, we present a new modification of the newly developed semi-analytical method named the Optimal Auxilary Function Method (OAFM) for fractional-order equations using the Caputo operator, which is named FOAFM. The mathematical theory of FOAFM is presented and the effectiveness of this method is proven by using it with well-known Fornberg-Whitham Equations (FWE). The FOAFM results are compared with other method results along with their exact solutions with the help of tables and plots to prove the validity of FOAFM. A rapidly convergent series solution is obtained from FOAFM and is validated by comparison with other results. The… More >

  • Open Access


    The Fractional Investigation of Fornberg-Whitham Equation Using an Efficient Technique

    Hassan Khan1,2, Poom Kumam3,4,*, Asif Nawaz1, Qasim Khan1, Shahbaz Khan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 259-273, 2023, DOI:10.32604/cmes.2022.021332

    Abstract In the last few decades, it has become increasingly clear that fractional calculus always plays a very significant role in various branches of applied sciences. For this reason, fractional partial differential equations (FPDEs) are of more importance to model the different physical processes in nature more accurately. Therefore, the analytical or numerical solutions to these problems are taken into serious consideration and several techniques or algorithms have been developed for their solution. In the current work, the idea of fractional calculus has been used, and fractional Fornberg Whitham equation (FFWE) is represented in its fractional view analysis. A well-known method… More >

  • Open Access


    He’s Homotopy Perturbation Method and Fractional Complex Transform for Analysis Time Fractional Fornberg-Whitham Equation

    Yanni Zhang1,2, Jing Pang1,2,*

    Sound & Vibration, Vol.55, No.4, pp. 295-303, 2021, DOI:10.32604/sv.2021.014445

    Abstract In this article, time fractional Fornberg-Whitham equation of He’s fractional derivative is studied. To transform the fractional model into its equivalent differential equation, the fractional complex transform is used and He’s homotopy perturbation method is implemented to get the approximate analytical solutions of the fractional-order problems. The graphs are plotted to analysis the fractional-order mathematical modeling. More >

  • Open Access


    Non Probabilistic Solution of Fuzzy Fractional Fornberg-Whitham Equation

    S. Chakraverty1,2, Smita Tapaswini1

    CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.2, pp. 71-90, 2014, DOI: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… More >

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