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Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method

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  • A. A. Hemeda

Abstract

An extension of the so‐called new iterative method (NIM) has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein‐Gordon equation, and fractional Boussinesq‐like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM) and the variational iteration method (VIM) reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.

Suggested Citation

  • A. A. Hemeda, 2013. "Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:717540
    DOI: 10.1155/2013/717540
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    References listed on IDEAS

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    1. Momani, Shaher & Abuasad, Salah, 2006. "Application of He’s variational iteration method to Helmholtz equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1119-1123.
    2. A. A. Hemeda, 2013. "New Iterative Method: An Application for Solving Fractional Physical Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. A. A. Hemeda, 2012. "Formulation and Solution of th-Order Derivative Fuzzy Integrodifferential Equation Using New Iterative Method with a Reliable Algorithm," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, October.
    4. A. A. Hemeda, 2013. "New Iterative Method: An Application for Solving Fractional Physical Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, May.
    5. A. A. Hemeda, 2012. "Formulation and Solution of nth‐Order Derivative Fuzzy Integrodifferential Equation Using New Iterative Method with a Reliable Algorithm," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. B. A. Jacobs & C. Harley, 2014. "Two Hybrid Methods for Solving Two‐Dimensional Linear Time‐Fractional Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. A. A. Hemeda & E. E. Eladdad, 2016. "Iterative Methods for Solving the Fractional Form of Unsteady Axisymmetric Squeezing Fluid Flow with Slip and No‐Slip Boundaries," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).
    3. Qinjun Li & Danyal Soybaş & Onur Alp Ilhan & Gurpreet Singh & Jalil Manafian, 2021. "Pure Traveling Wave Solutions for Three Nonlinear Fractional Models," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).

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