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A note on analytical solutions of nonlinear fractional 2D heat equation with non-local integral terms

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Abstract

In this paper, we consider the (2+1) nonlinear fractional heat equation with non-local integral terms and investigate two different cases of such non-local integral terms. The first has to do with the time-dependent non-local integral term and the second is the space-dependent non-local integral term. Apart from the nonlinear nature of these formulations, the complexity due to the presence of the non-local integral terms impelled us to use a relatively new analytical technique called q-homotopy analysis method to obtain analytical solutions to both cases in the form of convergent series with easily computable components. Our numerical analysis enables us to show the effects of non-local terms and the fractional-order derivative on the solutions obtained by this method.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Wisconsin, USA

    O S IYIOLA

  2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, KFUPM, Dhahran, Saudi Arabia

    F D ZAMAN

Authors
  1. O S IYIOLA
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  2. F D ZAMAN
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Correspondence to O S IYIOLA.

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IYIOLA, O.S., ZAMAN, F.D. A note on analytical solutions of nonlinear fractional 2D heat equation with non-local integral terms. Pramana - J Phys 87, 51 (2016). https://doi.org/10.1007/s12043-016-1239-1

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  • DOI: https://doi.org/10.1007/s12043-016-1239-1

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