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  • 1.
    Karbalaie, Abdolamir
    et al.
    KTH, Informatik, logistik och management.
    Montazeri, M. M.
    Hamid Muhammed, Hamed
    KTH, Informatik, logistik och management.
    New approach to find the exact solution of fractional partial differential equation2012In: WSEAS Transactions on Mathematics, ISSN 1109-2769, E-ISSN 2224-2880, Vol. 11, no 10, p. 908-917Article in journal (Refereed)
    Abstract [en]

    In this study, we present the exact solution of certain fractional partial differential equations (FPDE) by using a modified homotopy perturbation method (MHPM).The exact solutions are constructed by choosing an appropriate initial approximation and only one term of the series obtained by MHPM. The exact solutions for initial value problems of FPDE are analytically derived. The methods introduced an efficient tool for solving a wide class of time-fractional partial differential equations.

  • 2.
    Karbalaie, Abdolamir
    et al.
    KTH, Systemsäkerhet och organisation.
    Montazeri, Mohammad M
    Islamic Azad University,Khomeini Shahr, Isfahan, Iran.
    Hamid Muhammed, Hamed
    KTH, Systemsäkerhet och organisation.
    Exact Solution of Time-Fractional Partial Differential Equations Using Sumudu Transform2014In: WSEAS Transactions on Mathematics, ISSN 1109-2769, E-ISSN 2224-2880, Vol. 13, p. 142-151Article in journal (Refereed)
    Abstract [en]

    Abstract: In this study, we propose a new algorithm to find exact solution of nonlinear time- fractional partialdifferential equations. The new algorithm basically illustrates how two powerful algorithms, the homotopy pertur-bation method and the Sumudu transform method can be combined and used to get exact solutions of fractionalpartial differential equations. We also present four different examples to illustrate the preciseness and effectivenessof this algorithm.

  • 3.
    Karbalaie, Abdolamir
    et al.
    KTH.
    MONTAZERI, MOHAMMAD MEHDI
    Khomeinishahr Branch Islamic Azad University Khomeinishahr, Isfahan.
    SHABANI, MARYAM
    Naghsh Jahan Intelligent and Communication Engineering Sahin Shahr, Isfahan IRAN.
    Erlandsson, Björn-Erik
    KTH.
    Application of Homo-separation of variables method on nonlinearsystem of PDEs2014In: WSEAS Transactions on Mathematics, ISSN 1109-2769, E-ISSN 2224-2880, Vol. 13, p. 992-1000Article in journal (Refereed)
    Abstract [en]

    In this study, the Homo-Separation of Variables method is introduced to find the exact solution of somecoupled nonlinear partial differential equations. This analytical method is a new combination of two powerfuland popular methods; namely the homotopy perturbation method (HPM) and the separation of variables method.The exact solution is constructed by choosing an appropriate initial approximation in addition to retaining onlythe first term of the series obtained by HPM. The proposed method is capable of reducing the computational loadconsiderably when compared to other classical method.

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