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Mathematical Problems in Engineering
Volume 2014, Article ID 705364, 7 pages
http://dx.doi.org/10.1155/2014/705364
Research Article

Fundamental Solutions to Time-Fractional Advection Diffusion Equation in a Case of Two Space Variables

Institute of Mathematics and Computer Science, Jan Długosz University in Częstochowa, Waszyngtona 4/8, 42-200 Częstochowa, Poland

Received 28 December 2013; Accepted 6 February 2014; Published 11 March 2014

Academic Editor: J. A. Tenreiro Machado

Copyright © 2014 Y. Z. Povstenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [12 citations]

The following is the list of published articles that have cited the current article.

  • Ali H. Bhrawy, Abdulrahim AlZahrani, Dumitru Baleanu, and Yahia Alhamed, “A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
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  • Yuriy Povstenko, and Tamara Kyrylych, “Two Approaches to Obtaining the Space-Time Fractional Advection-Diffusion Equation,” Entropy, vol. 19, no. 7, pp. 297, 2017. View at Publisher · View at Google Scholar
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  • Xian-Ming Gu, Ting-Zhu Huang, Cui-Cui Ji, Bruno Carpentieri, and Anatoly A. Alikhanov, “Fast Iterative Method with a Second-Order Implicit Difference Scheme for Time-Space Fractional Convection–Diffusion Equation,” Journal of Scientific Computing, 2017. View at Publisher · View at Google Scholar
  • Itrat Abbas Mirza, and Dumitru Vieru, “Fundamental solutions to advection–diffusion equation with time-fractional Caputo–Fabrizio derivative,” Computers & Mathematics with Applications, vol. 73, no. 1, pp. 1–10, 2017. View at Publisher · View at Google Scholar
  • Derya Avci, Beyza Billur Iskender Eroglu, and Necati Ozdemir, “The dirichlet problem of a conformable advection-diffusion equation,” Thermal Science, vol. 21, pp. 9–18, 2017. View at Publisher · View at Google Scholar
  • Slawomir Blasiak, “Time-Fractional Fourier Law in a finite hollow cylinder under Gaussian-distributed heat flux,” EPJ Web of Conferences, vol. 180, pp. 02008, 2018. View at Publisher · View at Google Scholar
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  • Derya Avcı, and Aylin Yetim, “Cauchy and source problems for an advection-diffusion equation with Atangana–Baleanu derivative on the real line,” Chaos, Solitons & Fractals, vol. 118, pp. 361–365, 2019. View at Publisher · View at Google Scholar