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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 806984, 4 pages
Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order
1School of Information Science & Technology, East China Normal University, No. 500, Dong-Chuan Road, Shanghai 200241, China
2Department of Computer and Information Science, University of Macau, Avenida Padre Tomas Pereira, Taipa, Macau
Received 21 April 2013; Accepted 10 May 2013
Academic Editor: Carlo Cattani
Copyright © 2013 Ming Li and Wei Zhao. 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 [10 citations]
The following is the list of published articles that have cited the current article.
- Yuan-Ming Wang, “Maximum Norm Error Estimates of ADI Methods for a Two-Dimensional Fractional Subdiffusion Equation,” Advances in Mathematical Physics, vol. 2013, pp. 1–10, 2013.
- Shaoxiang Hu, “External Fractional-Order Gradient Vector Perona-Malik Diffusion for Sinogram Restoration of Low-Dosed X-Ray Computed Tomography,” Advances in Mathematical Physics, vol. 2013, pp. 1–10, 2013.
- Shu-Li Mei, and De-Hai Zhu, “Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation,” Advances in Mathematical Physics, vol. 2013, pp. 1–12, 2013.
- Gabriel Bengochea, “Operational solution of fractional differential equations,” Applied Mathematics Letters, 2014.
- Salman Jahanshahi, Esmail Babolian, Delfim F.M. Torres, and Alireza Vahidi, “Solving Abel integral equations of first kind via fractional calculus,” Journal of King Saud University - Science, 2014.
- Yi-Ming Chen, Yan-Qiao Wei, Da-Yan Liu, and Hao Yu, “Numerical solution for a class of nonlinear variable order fractional differential equations with Legendre wavelets,” Applied Mathematics Letters, 2015.
- Gabriel Bengochea, and Manuel D. Ortigueira, “An operational approach to solve fractional continuous–time linear systems,” International Journal of Dynamics and Control, 2015.
- Mohamed S. Mohamed, Khaled A. Gepreel, Faisal A. Al-Malki, and Maha Al-Humyani, “Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method,” Journal of Applied Mathematics, vol. 2015, pp. 1–9, 2015.
- Valery Sizikov, and Denis Sidorov, “Generalized quadrature for solving singular integral equations of Abel type in application to infrared tomography,” Applied Numerical Mathematics, vol. 106, pp. 69–78, 2016.
- Yi-Ming Chen, Yan-Qiao Wei, Da-Yan Liu, Driss Boutat, and Xiu-Kai Chen, “Variable-order fractional numerical differentiation for noisy signals by wavelet denoising,” Journal of Computational Physics, vol. 311, pp. 338–347, 2016.