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Time‐Space Fractional Heat Equation in the Unit Disk

Author

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  • Rabha W. Ibrahim
  • Hamid A. Jalab

Abstract

We will study a maximal solution of the time‐space fractional heat equation in complex domain. The fractional time is taken in the sense of the Riemann‐Liouville operator, while the fractional space is assumed in the Srivastava‐Owa operator. Here we employ some properties of the univalent functions in the unit disk to determine the upper bound of this solution. The maximal solution is illustrated in terms of the generalized hypergeometric functions.

Suggested Citation

  • Rabha W. Ibrahim & Hamid A. Jalab, 2013. "Time‐Space Fractional Heat Equation in the Unit Disk," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:364042
    DOI: 10.1155/2013/364042
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    References listed on IDEAS

    as
    1. Rabha W. Ibrahim, 2012. "Ulam Stability for Fractional Differential Equation in Complex Domain," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Rabha W. Ibrahim, 2012. "Ulam Stability for Fractional Differential Equation in Complex Domain," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-8, January.
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