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Computational Solution of a Fractional Integro‐Differential Equation

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  • Muhammet Kurulay
  • Mehmet Ali Akinlar
  • Ranis Ibragimov

Abstract

Although differential transform method (DTM) is a highly efficient technique in the approximate analytical solutions of fractional differential equations, applicability of this method to the system of fractional integro‐differential equations in higher dimensions has not been studied in detail in the literature. The major goal of this paper is to investigate the applicability of this method to the system of two‐dimensional fractional integral equations, in particular to the two‐dimensional fractional integro‐Volterra equations. We deal with two different types of systems of fractional integral equations having some initial conditions. Computational results indicate that the results obtained by DTM are quite close to the exact solutions, which proves the power of DTM in the solutions of these sorts of systems of fractional integral equations.

Suggested Citation

  • Muhammet Kurulay & Mehmet Ali Akinlar & Ranis Ibragimov, 2013. "Computational Solution of a Fractional Integro‐Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:865952
    DOI: 10.1155/2013/865952
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    References listed on IDEAS

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    1. B. Bandrowski & A. Karczewska & P. Rozmej, 2012. "Numerical Solutions to Fractional Perturbed Volterra Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Abdelouahab Kadem & Adem Kilicman, 2012. "The Approximate Solution of Fractional Fredholm Integrodifferential Equations by Variational Iteration and Homotopy Perturbation Methods," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. B. Bandrowski & A. Karczewska & P. Rozmej, 2012. "Numerical Solutions to Fractional Perturbed Volterra Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, December.
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