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Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes

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  • Abdon Atangana
  • Dumitru Baleanu

Abstract

A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this time‐fractional parabolic equation with two difference schemes. The explicit and the implicit schemes in this case are stable under some conditions.

Suggested Citation

  • Abdon Atangana & Dumitru Baleanu, 2013. "Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:828764
    DOI: 10.1155/2013/828764
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    References listed on IDEAS

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    1. Ali Yakar & Mehmet Emir Koksal, 2012. "Existence Results for Solutions of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Abdon Atangana & Aydin Secer, 2013. "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    3. Ali Yakar & Mehmet Emir Koksal, 2012. "Existence Results for Solutions of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, May.
    4. Abdon Atangana & Aydin Secer, 2013. "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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    Cited by:

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    2. Qazi Mahmood Ul Hassan & Jamshad Ahmad & Muhammad Shakeel, 2014. "A Novel Analytical Technique to Obtain Kink Solutions for Higher Order Nonlinear Fractional Evolution Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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