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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 291386, 5 pages
Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System
1College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130061, China
2Electronic and Information Technology Department, Jiangmen Polytechnic, Jiangmen 529090, China
3Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou Campus, Xuzhou, Jiangsu 221008, China
Received 23 July 2013; Revised 7 August 2013; Accepted 12 August 2013
Academic Editor: D. Băleanu
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.
Citations to this Article [15 citations]
The following is the list of published articles that have cited the current article.
- Ali H. Bhrawy, Yahia A. Alhamed, Dumitru Baleanu, and Abdulrahim A. Al-Zahrani, “New spectral techniques for systems of fractional differential equations using fractional-order generalized Laguerre orthogonal functions,” Fractional Calculus and Applied Analysis, vol. 17, no. 4, pp. 1137–1157, 2014.
- Ai-Min Yang, Yu-Zhu Zhang, Carlo Cattani, Gong-Nan Xie, Mohammad Mehdi Rashidi, Yi-Jun Zhou, and Xiao-Jun Yang, “Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets,” Abstract and Applied Analysis, vol. 2014, pp. 1–6, 2014.
- Chun-Guang Zhao, Ai-Min Yang, Hossein Jafari, and Ahmad Haghbin, “The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative,” Abstract and Applied Analysis, vol. 2014, pp. 1–5, 2014.
- A. H. Bhrawy, and M. A. Alghamdi, “A Shifted Jacobi-Gauss Collocation Scheme for Solving Fractional Neutral Functional-Differential Equations,” Advances in Mathematical Physics, vol. 2014, pp. 1–8, 2014.
- A. H. Bhrawy, “A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation,” Abstract and Applied Analysis, vol. 2014, pp. 1–10, 2014.
- Huixia Mo, Xin Sui, and Dongyan Yu, “Generalized Convex Functions on Fractal Sets and Two Related Inequalities,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014.
- 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.
- Wei Wei, H. M. Srivastava, Yunyi Zhang, Lei Wang, Peiyi Shen, and Jing Zhang, “A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014.
- Adem Kılıçman, and Wedad Saleh, “Some generalized Hermite-Hadamard type integral inequalities for generalized s-convex functions on fractal sets,” Advances in Difference Equations, vol. 2015, no. 1, 2015.
- Adem Kılıçman, and Wedad Saleh, “Notions of generalized s-convex functions on fractal sets,” Journal of Inequalities and Applications, vol. 2015, no. 1, 2015.
- Sheng-Ping Yan, “Local Fractional Laplace Series Expansion Method For Diffusion Equation Arising In Fractal Heat Transfer,” Thermal Science, vol. 19, pp. S131–S135, 2015.
- Ai-Min Yang, Jie Li, Yu-Zhu Zhang, and Wei-Xing Liu, “A New Coupling Schedule For Series Expansion Method And Sumudu Transform With An Applications To Diffusion Equation In Fractal Heat Transfer,” Thermal Science, vol. 19, pp. S145–S149, 2015.
- Syed Tauseef Mohyud-Din, Naveed Ahmed, Asif Waheed, Muhammad Ali Akbar, and Umar Khan, “Solutions Of Fractional Diffusion Equations By Variation Of Parameters Method,” Thermal Science, vol. 19, pp. S69–S75, 2015.
- Jagdev Singh, Devendra Kumar, and Juan Nieto, “A Reliable Algorithm for a Local Fractional Tricomi Equation Arising in Fractal Transonic Flow,” Entropy, vol. 18, no. 6, pp. 206, 2016.
- Maohua Ran, and Chengjian Zhang, “A conservative difference scheme for solving the strongly coupled nonlinear fractional Schrödinger equations,” Communications in Nonlinear Science and Numerical Simulation, 2016.