- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
International Journal of Differential Equations
Volume 2012 (2012), Article ID 154085, 13 pages
Axisymmetric Solutions to Time-Fractional Heat Conduction Equation in a Half-Space under Robin Boundary Conditions
1Institute of Mathematics and Computer Science, Jan Dlugosz University, 42200 Czestochowa, Poland
2Department of Computer Science, European University of Informatics and Economics (EWSIE), 03741 Warsaw, Poland
Received 23 May 2012; Revised 18 July 2012; Accepted 23 July 2012
Academic Editor: Nikolai Leonenko
Copyright © 2012 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.
- Y. Z. Povstenko, “Fractional heat conduction equation and associated thermal stress,” Journal of Thermal Stresses, vol. 28, no. 1, pp. 83–102, 2005.
- Y. Z. Povstenko, “Theory of thermoelasticity based on the space-time-fractional heat conduction equation,” Physica Scripta, vol. T136, Article ID 014017, 6 pages, 2009.
- R. Gorenflo, F. Mainardi, D. Moretti, and P. Paradisi, “Time fractional diffusion: a discrete random walk approach,” Nonlinear Dynamics, vol. 29, no. 1–4, pp. 129–143, 2002.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, Switzerland, 1993.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006.
- R. Gorenflo and F. Mainardi, “Fractional calculus: integral and differential equations of fractional order,” in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, Eds., vol. 378 of CISM Courses and Lectures, pp. 223–276, Springer, Vienna, 1997.
- Y. Povstenko, “Non-axisymmetric solutions to time-fractional diffusion-wave equation in an infinite cylinder,” Fractional Calculus and Applied Analysis, vol. 14, no. 3, pp. 418–435, 2011.
- W. Wyss, “The fractional diffusion equation,” Journal of Mathematical Physics, vol. 27, no. 11, pp. 2782–2785, 1986.
- W. R. Schneider and W. Wyss, “Fractional diffusion and wave equations,” Journal of Mathematical Physics, vol. 30, no. 1, pp. 134–144, 1989.
- F. Mainardi, “The fundamental solutions for the fractional diffusion-wave equation,” Applied Mathematics Letters, vol. 9, no. 6, pp. 23–28, 1996.
- F. Mainardi, “Fractional relaxation-oscillation and fractional diffusion-wave phenomena,” Chaos, Solitons and Fractals, vol. 7, no. 9, pp. 1461–1477, 1996.
- R. Gorenflo and F. Mainardi, “Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations,” Matimyás Matematika, vol. 21, pp. 109–118, 1998.
- A. Hanyga, “Multidimensional solutions of time-fractional diffusion-wave equations,” Proceedings of the Royal Society A, vol. 458, no. 2020, pp. 933–957, 2002.
- S. D. Eidelman and A. N. Kochubei, “Cauchy problem for fractional diffusion equations,” Journal of Differential Equations, vol. 199, no. 2, pp. 211–255, 2004.
- Y. Luchko, “Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation,” Computers & Mathematics with Applications, vol. 59, no. 5, pp. 1766–1772, 2010.
- J.-H. He, “Approximate analytical solution for seepage flow with fractional derivatives in porous media,” Computer Methods in Applied Mechanics and Engineering, vol. 167, no. 1-2, pp. 57–68, 1998.
- J.-H. He, “A short remark on fractional variational iteration method,” Physics Letters A, vol. 375, no. 38, pp. 3362–3364, 2011.
- J.-H. He, S. K. Elagan, and Z. B. Li, “Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus,” Physics Letters A, vol. 376, no. 4, pp. 257–259, 2012.
- A. K. Bazzaev and M. Kh. Shkhanukov-Lafishev, “Locally one-dimensional scheme for fractional diffusion equation with Robin boundary conditions,” Computational Mathematics and Mathematical Physics, vol. 50, no. 7, pp. 1141–1149, 2010.
- J. Kemppainen, “Existence and uniqueness of the solution for a time-fractional diffusion equation with Robin boundary condition,” Abstract and Applied Analysis, vol. 2011, Article ID 321903, 11 pages, 2011.
- Y. Povstenko, “Time-fractional radial heat conduction in a cylinder and associated thermal stresses,” Archive of Applied Mechanics, vol. 82, no. 3, pp. 345–362, 2012.
- Y. Z. Povstenko, “Central symmetric solution to the Neumann problem for a time-fractional diffusion-wave equation in a sphere,” Nonlinear Analysis: Real World Applications, vol. 13, no. 3, pp. 1229–1238, 2012.
- X. Yang, “Local fractional integral transforms,” Progress in Nonlinear Science, vol. 4, pp. 1–225, 2011.
- A. S. Galitsyn and A. N. Zhovsky, Integral Transforms and Special Functions in Heat Conduction Problems, Naukova Dumka, Kiev, Ukraine, 1976 (Russian).
- A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions, Nauka, Moscow, Russia, 1983 (Russian).
- A. Erdélyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Tables of Integral Transforms, vol. 1, McGraw-Hill, New York, NY, USA, 1954.