Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Kumam, PoomSubject: search.filters.subject.Adomian Decomposition Method

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 37
    Citation - Scopus: 48
    An Approximate Analytical Solution of the Navier-Stokes Equations Within Caputo Operator and Elzaki Transform Decomposition Method
    (Springer, 2020) Khan, Hassan; Khan, Adnan; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; Hajira
    In this article, a hybrid technique of Elzaki transformation and decomposition method is used to solve the Navier-Stokes equations with a Caputo fractional derivative. The numerical simulations and examples are presented to show the validity of the suggested method. The solutions are determined for the problems of both fractional and integer orders by a simple and straightforward procedure. The obtained results are shown and explained through graphs and tables. It is observed that the derived results are very close to the actual solutions of the problems. The fractional solutions are of special interest and have a strong relation with the solution at the integer order of the problems. The numerical examples in this paper are nonlinear and thus handle its solutions in a sophisticated manner. It is believed that this work will make it easy to study the nonlinear dynamics, arising in different areas of research and innovation. Therefore, the current method can be extended for the solution of other higher-order nonlinear problems.
  • Article
    Citation - WoS: 37
    Citation - Scopus: 40
    The Analytical Investigation of Time-Fractional Multi-Dimensional Navier-Stokes Equation
    (Elsevier, 2020) Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Shah, Rasool
    In the present research article, we implemented two well-known analytical techniques to solve fractional-order multi-dimensional Navier-Stokes equation. The proposed methods are the modification of Adomian decomposition method and variational iteration method by using natural transformation. Furthermore, some illustrative examples are presented to confirm the validity of the suggested methods. The solutions graphs and tables are constructed for both fractional and integer-order problems. It is investigated that the suggested techniques have the identical solutions of the problems. The solution comparison via graphs and tables have also supported the greater accuracy and higher rate of convergence of the present methods. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 7
    An Approximate-Analytical Solution To Analyze Fractional View of Telegraph Equations
    (Ieee-inst Electrical Electronics Engineers inc, 2020) Khan, Hassan; Farooq, Umar; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Ali, Izaz
    In the present research article, a modified analytical method is applied to solve time-fractional telegraph equations. The Caputo-operator is used to express the derivative of fractional-order. The present method is the combination of two well-known methods namely Mohan transformation method and Adomian decomposition method. The validity of the proposed technique is confirmed through illustrative examples. It is observed that the obtained solutions have strong contact with the exact solution of the examples. Moreover, it is investigated that the present method has the desired degree of accuracy and provided the graphs closed form solutions of all targeted examples. The graphs have verified the convergence analysis of fractional-order solutions to integer-order solution. In conclusion, the suggested method is simple, straightforward and an effective technique to solve fractional-order partial differential equations.
  • Article
    Citation - WoS: 32
    Citation - Scopus: 38
    A Novel Method for the Analytical Solution of Fractional Zakharov-Kuznetsov Equations
    (Springer, 2019) Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Shah, Rasool
    In this article, an efficient analytical technique, called Laplace-Adomian decomposition method, is used to obtain the solution of fractional Zakharov- Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.