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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 316978, 6 pages
Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators
1Electronic and Information Technology Department, Jiangmen Polytechnic, Jiangmen 529090, China
2College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130061, China
3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
4Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
5Institute of Space Sciences, Magurele, 077125 Bucharest, Romania
6Mihail Sadoveanu Theoretical High School, District 2, Street Popa Lazar No. 8, 021586 Bucharest, Romania
7Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou Campus, Xuzhou, Jiangsu 221008, China
Received 27 August 2013; Accepted 24 September 2013
Academic Editor: Ali H. Bhrawy
Copyright © 2013 Yang Zhao 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.
- G. E. Andrews, R. Askey, and R. Roy, Special Functions, Cambridge University Press, Cambridge, UK, 1999.
- Á. Elbert and A. Laforgia, “On some properties of the gamma function,” Proceedings of the American Mathematical Society, vol. 128, no. 9, pp. 2667–2673, 2000.
- N. Virchenko, S. L. Kalla, and A. Al-Zamel, “Some results on a generalized hypergeometric function,” Integral Transforms and Special Functions, vol. 12, no. 1, pp. 89–100, 2001.
- J. Choi and P. Agarwal, “Certain unified integrals associated with Bessel functions,” Boundary Value Problems, vol. 2013, no. 1, pp. 1–9, 2013.
- P. J. McNamara, “Metaplectic Whittaker functions and crystal bases,” Duke Mathematical Journal, vol. 156, no. 1, pp. 1–31, 2011.
- E. W. Barnes, “The theory of the G-function,” Quarterly Journal of Mathematics, vol. 31, pp. 264–314, 1899.
- R. Floreanini and L. Vinet, “ and -special functions,” Contemporary Mathematics, vol. 160, p. 85, 1994.
- H. M. Srivastava, K. C. Gupta, and S. P. Goyal, The H-Functions of One and Two Variables with Applications, South Asian Publishers, New Delhi, India, 1982.
- R. Gorenflo, A. A. Kilbas, and S. V. Rogosin, “On the generalized Mittag-Leffler type functions,” Integral Transforms and Special Functions, vol. 7, no. 3-4, pp. 215–224, 1998.
- R. K. Saxena and M. Saigo, “Certain properties of fractional calculus operators associated with generalized Mittag-Leffler function,” Fractional Calculus & Applied Analysis, vol. 8, no. 2, pp. 141–154, 2005.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos, World Scientific, Singapore, 2012.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Elsevier, Amsterdam, The Netherlands, 2006.
- J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, New York, NY, USA, 2007.
- S. Hu, Y. Q. Chen, and T. S. Qiu, Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications, Springer, New York, NY, USA, 2012.
- F. Mainardi and R. Gorenflo, “On Mittag-Leffler-type functions in fractional evolution processes,” Journal of Computational and Applied Mathematics, vol. 118, no. 1-2, pp. 283–299, 2000.
- R. K. Saxena, A. M. Mathai, and H. J. Haubold, “Fractional reaction-diffusion equations,” Astrophysics and Space Science, vol. 305, no. 3, pp. 289–296, 2006.
- Y. Li, Y. Chen, and I. Podlubny, “Mittag-Leffler stability of fractional order nonlinear dynamic systems,” Automatica, vol. 45, no. 8, pp. 1965–1969, 2009.
- E. C. de Oliveira, F. Mainardi, and J. Vaz Jr., “Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics,” The European Physical Journal Special Topics, vol. 193, no. 1, pp. 161–171, 2011.
- D. S. F. Crothers, D. Holland, Y. P. Kalmykov, and W. T. Coffey, “The role of Mittag-Leffler functions in anomalous relaxation,” Journal of Molecular Liquids, vol. 114, no. 1-3, pp. 27–34, 2004.
- E. Scalas, R. Gorenflo, and F. Mainardi, “Fractional calculus and continuous-time finance,” Physica A, vol. 284, no. 1–4, pp. 376–384, 2000.
- B. N. N. Achar and J. W. Hanneken, “Fractional radial diffusion in a cylinder,” Journal of Molecular Liquids, vol. 114, no. 1–3, pp. 147–151, 2004.
- S. J. Sadati, D. Baleanu, A. Ranjbar, R. Ghaderi, and T. Abdeljawad, “Mittag-Leffler stability theorem for fractional nonlinear systems with delay,” Abstract and Applied Analysis, vol. 2010, Article ID 108651, 7 pages, 2010.
- S. W. J. Welch, R. A. L. Rorrer, and R. G. Duren Jr., “Application of time-based fractional calculus methods to viscoelastic creep and stress relaxation of materials,” Mechanics Time-Dependent Materials, vol. 3, no. 3, pp. 279–303, 1999.
- X. J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher, Hong Kong, China, 2011.
- X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science, New York, NY, USA, 2012.
- M.-S. Hu, R. P. Agarwal, and X.-J. Yang, “Local fractional Fourier series with application to wave equation in fractal vibrating string,” Abstract and Applied Analysis, vol. 2012, Article ID 567401, 15 pages, 2012.
- Y. Zhang, A. Yang, and X.-J. Yang, “1-D heat conduction in a fractal medium: a solution by the local fractional Fourier series method,” Thermal Science, vol. 17, no. 3, pp. 953–956, 2013.
- Y.-J. Yang, D. Baleanu, and X.-J. Yang, “Analysis of fractal wave equations by local fractional Fourier series method,” Advances in Mathematical Physics, vol. 2013, Article ID 632309, 6 pages, 2013.
- X. J. Yang, D. Baleanu, and J. A. T. Machado, “Mathematical aspects of Heisenberg uncertainty principle within local fractional Fourier analysis,” Boundary Value Problems, vol. 2013, no. 1, pp. 131–146, 2013.
- A. M. Yang, Y. Z. Zhang, and Y. Long, “The Yang-Fourier transforms to heat-conduction in a semi-infinite fractal bar,” Thermal Science, vol. 17, no. 3, pp. 707–7713, 2013.
- F. Gao, W. P. Zhong, and X. M. Shen, “Applications of Yang-Fourier transform to local fractional equations with local fractional derivative and local fractional integral,” Advanced Materials Research, vol. 461, pp. 306–310, 2012.
- J.-H. He, “Asymptotic methods for solitary solutions and compactons,” Abstract and Applied Analysis, vol. 2012, Article ID 916793, 130 pages, 2012.
- C. F. Liu, S. S. Kong, and S. J. Yuan, “Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem,” Thermal Science, vol. 17, no. 3, pp. 715–721, 2013.
- G. S. Chen, “Generalizations of hölder’s and some related integral inequalities on fractal space,” Journal of Function Spaces and Applications, vol. 2013, Article ID 198405, 9 pages, 2013.
- A. Carpinteri, B. Chiaia, and P. Cornetti, “The elastic problem for fractal media: basic theory and finite element formulation,” Computers and Structures, vol. 82, no. 6, pp. 499–508, 2004.
- A. K. Golmankhaneh, V. Fazlollahi, and D. Baleanu, “Newtonian mechanics on fractals subset of real-line,” Romania Reports in Physics, vol. 65, pp. 84–93, 2013.