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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 590574, 5 pages
Local Fractional Poisson and Laplace Equations with Applications to Electrostatics in Fractal Domain
1Northeast Institute of Geography and Agroecology, Chinese Academy of Sciences, Changchun 130102, China
2University of Chinese Academy of Sciences, Beijing 100049, China
3Electronic and Information Technology Department, Jiangmen Polytechnic, Jiangmen 529090, China
4School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi 710048, China
5Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
6Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
7Institute of Space Sciences, Magurele, 077125 Bucharest, Romania
8Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China
Received 19 March 2014; Accepted 1 April 2014; Published 16 April 2014
Academic Editor: Carlo Cattani
Copyright © 2014 Yang-Yang Li et al. 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.
- D. J. Griffiths and C. Reed, Introduction to Electrodynamics, Prentice Hall, Upper Saddle River, NJ, USA, 1999.
- M. N. Sadiku, Numerical Techniques in Electromagnetic, CRC Press, 2000.
- D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, Germany, 2001.
- E. M. Poliščuk, “Equations of the Laplace and Poisson type in a function space,” Matematicheskii Sbornik, vol. 114, no. 2, pp. 261–292, 1967.
- S. Persides, “The Laplace and Poisson equations in Schwarzschild's space-time,” Journal of Mathematical Analysis and Applications, vol. 43, pp. 571–578, 1973.
- J. Eve and H. I. Scoins, “A note on the approximate solution of the equations of Poisson and Laplace by finite difference methods,” The Quarterly Journal of Mathematics, vol. 7, pp. 217–223, 1956.
- J. Franz and M. Kasper, “Superconvergent finite element solutions of laplace and poisson equation,” IEEE Transactions on Magnetics, vol. 32, no. 3, pp. 643–646, 1996.
- M. K. Chati, M. D. Grigoriu, S. S. Kulkarni, and S. Mukherjee, “Random walk method for the two- and three-dimensional Laplace, Poisson and Helmholtz's equations,” International Journal for Numerical Methods in Engineering, vol. 51, no. 10, pp. 1133–1156, 2001.
- A. C. Poler, A. W. Bohannon, S. J. Schowalter, and T. V. Hromadka, II, “Using the complex polynomial method with Mathematica to model problems involving the Laplace and Poisson equations,” Numerical Methods for Partial Differential Equations, vol. 25, no. 3, pp. 657–667, 2009.
- B. B. Mandelbrot, The Fractal Geometry of Nature, Macmillan, 1983.
- B. J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators, Springer, New York, NY, USA, 2003.
- E. Goldfain, “Fractional dynamics, Cantorian space-time and the gauge hierarchy problem,” Chaos, Solitons and Fractals, vol. 22, no. 3, pp. 513–520, 2004.
- V. E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, 2011.
- X.-J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science, New York, NY, USA, 2012.
- J. A. T. Machado, D. Baleanu, and A. C. J. Luo, Discontinuity and Complexity in Nonlinear Physical Systems, Springer, 2014.
- X.-J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic, Hong Kong, 2011.
- N. Engheta, “On the role of fractional calculus in electromagnetic theory,” IEEE Antennas and Propagation Magazine, vol. 39, no. 4, pp. 35–46, 1997.
- V. E. Tarasov, “Multipole moments of fractal distribution of charges,” Modern Physics Letters B, vol. 19, no. 22, pp. 1107–1118, 2005.
- G. Calcagni, J. Magueijo, and D. R. Fernández, “Varying electric charge in multiscale spacetimes,” Physical Review D, vol. 89, no. 2, Article ID 024021, 2014.
- Y. Zhao, D. Baleanu, C. Cattani, D.-F. Cheng, and X.-J. Yang, “Maxwell's equations on Cantor sets: a local fractional approach,” Advances in High Energy Physics, Article ID 686371, 6 pages, 2013.
- X.-J. Yang, D. Baleanu, and J. A. T. Machado, “Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis,” Boundary Value Problems, vol. 2013, no. 1, article 131, 16 pages, 2013.
- X.-J. Yang, D. Baleanu, and J. A. Tenreiro Machado, “Systems of Navier-Stokes equations on Cantor sets,” Mathematical Problems in Engineering, vol. 2013, Article ID 769724, 8 pages, 2013.
- A. M. Yang, C. Cattani, C. Zhang, G. N. Xie, and X.-J. Yang, “Local fractional Fourier series solutions for nonhomogeneous heat equations arising in fractal heat flow with local fractional derivative,” Advances in Mechanical Engineering, vol. 2014, Article ID 514639, 5 pages, 2014.
- C.-Y. Long, Y. Zhao, and H. Jafari, “Mathematical models arising in the fractal forest gap via local fractional calculus,” Abstract and Applied Analysis, vol. 2014, Article ID 782393, 6 pages, 2014.
- X.-J. Yang, H. M. Srivastava, J.-H. He, and D. Baleanu, “Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives,” Physics Letters A, vol. 377, no. 28–30, pp. 1696–1700, 2013.