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Space-Time-Fractional Advection Diffusion Equation in a Plane

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Advances in Modelling and Control of Non-integer-Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 320))

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Abstract

The fundamental solution to the Cauchy problem for the space-time-fractional advection diffusion equation with the Caputo time-fractional derivative and Riesz fractional Laplace operator is considered in a case of two spatial variables. The solution is obtained using the Laplace integral transform with respect to time t and the double Fourier transform with respect to space variables x and y. Several particular cases of the solution are analyzed in details. Numerical results are illustrated graphically.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Jan Dlugosz University in Czȩstochowa, Armii Krajowej 13/15, 42-200, Czȩstochowa, Poland

    Yuriy Povstenko

Authors
  1. Yuriy Povstenko
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Correspondence to Yuriy Povstenko .

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Editors and Affiliations

  1. Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland

    Krzysztof J. Latawiec

  2. Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland

    Marian Łukaniszyn

  3. Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland

    Rafał Stanisławski

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Povstenko, Y. (2015). Space-Time-Fractional Advection Diffusion Equation in a Plane. In: Latawiec, K., Łukaniszyn, M., Stanisławski, R. (eds) Advances in Modelling and Control of Non-integer-Order Systems. Lecture Notes in Electrical Engineering, vol 320. Springer, Cham. https://doi.org/10.1007/978-3-319-09900-2_26

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  • DOI: https://doi.org/10.1007/978-3-319-09900-2_26

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09899-9

  • Online ISBN: 978-3-319-09900-2

  • eBook Packages: EngineeringEngineering (R0)

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