Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Author: search.filters.author.Singh, JagdevPublisher: search.filters.publisher.Springer Heidelberg

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  • Article
    Citation - WoS: 100
    Citation - Scopus: 122
    A New Analysis of the Fornberg-Whitham Equation Pertaining To a Fractional Derivative With Mittag-Leffler Kernel
    (Springer Heidelberg, 2018) Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra
    The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.
  • Article
    Citation - WoS: 102
    Citation - Scopus: 119
    Analysis of a Fractional Model of the Ambartsumian Equation
    (Springer Heidelberg, 2018) Singh, Jagdev; Baleanu, Dumitru; Rathore, Sushila; Kumar, Devendra
    The prime target of this work is to investigate a fractional model of the Ambartsumian equation. This equation is very useful to describe the surface brightness of the Milky Way. The Ambartsumian equation of fractional order is solved with the aid of the HATM. The solution is presented in terms of the power series, which is convergent for all real values of variables and parameters. The outcomes drawn with the help of the HATM are presented in the form of graphs.