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Multidimensional Time Fractional Diffusion Equation

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Abstract

In this paper we present integral and series representations for the fundamental solution of the time fractional diffusion equation in an arbitrary dimension. The series representation obtained depends on the parity of the dimension. As an application of our results we study the diffusion and stress in the axially symmetric case for plane deformation associated with generalized thermoelasticity theory.

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Acknowledgements

The authors were supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”), within project UID/MAT/ 0416/2013. N. Vieira is Auxiliar Researcher, under the FCT Researcher Program 2014 (Ref: IF/00271/2014).

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Authors and Affiliations

  1. School of Technology and Management, Polytechnic Institute of Leiria, P-2411-901, Leiria, Portugal

    M. Ferreira

  2. CIDMA - Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

    M. Ferreira & N. Vieira

Authors
  1. M. Ferreira
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  2. N. Vieira
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Corresponding author

Correspondence to M. Ferreira .

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Editors and Affiliations

  1. Department of Mathematics, The University of Tulsa, Tulsa, Oklahoma, USA

    Christian Constanda

  2. Department of Mathematics, The University of Tulsa, Tulsa, Oklahoma, USA

    Matteo Dalla Riva

  3. Department of Mathematics, University of Padova, Padova, Italy

    Pier Domenico Lamberti

  4. Systems Analysis, Prognosis and Control, Fraunhofer Institute for Industrial Math, Kaiserslautern, Germany

    Paolo Musolino

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Ferreira, M., Vieira, N. (2017). Multidimensional Time Fractional Diffusion Equation. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59384-5_10

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