• Title/Summary/Keyword: Variation iteration method (VIM)

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A STUDY ON SINGULAR INTEGRO-DIFFERENTIAL EQUATION OF ABEL'S TYPE BY ITERATIVE METHODS

  • Behzadi, Sh.S.;Abbasbandy, S.;Allahviranloo, T.
    • Journal of applied mathematics & informatics
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    • v.31 no.3_4
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    • pp.499-511
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    • 2013
  • In this article, Adomian decomposition method (ADM), variation iteration method(VIM) and homotopy analysis method (HAM) for solving integro-differential equation with singular kernel have been investigated. Also,we study the existence and uniqueness of solutions and the convergence of present methods. The accuracy of the proposed method are illustrated with solving some numerical examples.

SOLVING FUZZY FRACTIONAL WAVE EQUATION BY THE VARIATIONAL ITERATION METHOD IN FLUID MECHANICS

  • KHAN, FIRDOUS;GHADLE, KIRTIWANT P.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.23 no.4
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    • pp.381-394
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    • 2019
  • In this paper, we are extending fractional partial differential equations to fuzzy fractional partial differential equation under Riemann-Liouville and Caputo fractional derivatives, namely Variational iteration methods, and this method have applied to the fuzzy fractional wave equation with initial conditions as in fuzzy. It is explained by one and two-dimensional wave equations with suitable fuzzy initial conditions.

SYSTEMATIC APPROXIMATION OF THREE DIMENSIONAL FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN FLUID MECHANICS

  • KHAN, FIRDOUS;GHADLE, KIRTIWANT P.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.23 no.3
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    • pp.253-266
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    • 2019
  • In this article, a systematic solution based on the sequence of expansion method is planned to solve the time-fractional diffusion equation, time-fractional telegraphic equation and time-fractional wave equation in three dimensions using a current and valid approximate method, namely the ADM, VIM, and the NIM subject to the estimate initial condition. By using these three methods it is likely to find the exact solutions or a nearby approximate solution of fractional partial differential equations. The exactness, efficiency, and convergence of the method are demonstrated through the three numerical examples.