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Invariant subspace and approximate analytic solutions of a fractional model of convective longitudinal fins in thermal conductivity

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Abstract.

In this work, a fractional model of convective longitudinal fins in thermal conductivity are studied by using the invariant subspace method (ISM). The method determines an invariant subspace and construct the exact solutions of the partial differential equations (PDEs) by reducing them to ordinary differential equations (ODEs). As a result of the calculations, exponential solutions of the model are derived. Furthermore, the two step Adomian decomposition method (TSADM) and the Padé approximation techniques are used to derive the Padé approximate solutions of the model. The are derived along with interesting figures showing both the exact and approximate solutions. Ultimately, for illustrating the acquired results, some numerical simulations are performed.

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou, China

    Aliyu Isa Aliyu

  2. Department of Mathematics, Faculty of Science, Federal University Dutse, Jigawa, Nigeria

    Aliyu Isa Aliyu

  3. Department of Mathematics, King Saud University, 11495, Riyadh, Saudi Arabia

    Maysaa Al-Qurashi

Authors
  1. Aliyu Isa Aliyu
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  2. Maysaa Al-Qurashi
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Correspondence to Aliyu Isa Aliyu.

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Aliyu, A.I., Al-Qurashi, M. Invariant subspace and approximate analytic solutions of a fractional model of convective longitudinal fins in thermal conductivity. Eur. Phys. J. Plus 134, 417 (2019). https://doi.org/10.1140/epjp/i2019-12808-6

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  • DOI: https://doi.org/10.1140/epjp/i2019-12808-6

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