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Solving PDEs of fractional order using the unified transform method

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  • Fernandez, Arran
  • Baleanu, Dumitru
  • Fokas, Athanassios S.

Abstract

We consider the unified transform method, also known as the Fokas method, for solving partial differential equations. We adapt and modify the methodology, incorporating new ideas where necessary, in order to apply it to solve a large class of partial differential equations of fractional order. We demonstrate the applicability of the method by implementing it to solve a model fractional problem.

Suggested Citation

  • Fernandez, Arran & Baleanu, Dumitru & Fokas, Athanassios S., 2018. "Solving PDEs of fractional order using the unified transform method," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 738-749.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:738-749
    DOI: 10.1016/j.amc.2018.07.061
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    References listed on IDEAS

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    1. Area, Iván & Losada, Jorge & Nieto, Juan J., 2016. "A note on the fractional logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 182-187.
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    Cited by:

    1. Dumitru Baleanu & Arran Fernandez & Ali Akgül, 2020. "On a Fractional Operator Combining Proportional and Classical Differintegrals," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    2. Taneco-Hernández, M.A. & Morales-Delgado, V.F. & Gómez-Aguilar, J.F., 2019. "Fundamental solutions of the fractional Fresnel equation in the real half-line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 807-827.
    3. Huseynov, Ismail T. & Ahmadova, Arzu & Fernandez, Arran & Mahmudov, Nazim I., 2021. "Explicit analytical solutions of incommensurate fractional differential equation systems," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    4. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    5. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    6. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

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