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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 737481, 12 pages
The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations
1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300 Bloemfontein, South Africa
2Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia
Received 4 March 2013; Accepted 16 April 2013
Academic Editor: Mustafa Bayram
Copyright © 2013 Abdon Atangana and Adem Kılıçman. 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 [14 citations]
The following is the list of published articles that have cited the current article.
- Abdon Atangana, and Adem Kilicman, “A Novel Integral Operator Transform and Its Application to Some FODE and FPDE with Some Kind of Singularities,” Mathematical Problems in Engineering, vol. 2013, pp. 1–7, 2013.
- Abdon Atangana, and Necdet Bildik, “The Use of Fractional Order Derivative to Predict the Groundwater Flow,” Mathematical Problems in Engineering, vol. 2013, pp. 1–9, 2013.
- Devendra Kumar, Jagdev Singh, and Sunil Kumar, “Numerical computation of fractional multi-dimensional diffusion equations by using a modified homotopy perturbation method,” Journal of the Association of Arab Universities for Basic and Applied Sciences, 2014.
- Faruk Uçar, “-Sumudu Transforms of -Analogues of Bessel Functions,” The Scientific World Journal, vol. 2014, pp. 1–7, 2014.
- Abdon Atangana, and Suares Clovis Noutchie Oukouomi, “Novel Approach for Dealing with Partial Differential Equations with Mixed Derivatives,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014.
- Abdon Atangana, Necdet Bildik, and S. C. Oukouomi Noutchie, “New Iteration Methods for Time-Fractional Modified Nonlinear Kawahara Equation,” Abstract and Applied Analysis, vol. 2014, pp. 1–9, 2014.
- B. A. Jacobs, and C. Harley, “Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations,” Abstract and Applied Analysis, vol. 2014, pp. 1–10, 2014.
- Sara H. M. Hamed, Eltayeb A. Yousif, and Arbab I. Arbab, “Analytic and Approximate Solutions of the Space-Time Fractional Schrödinger Equations by Homotopy Perturbation Sumudu Transform Method,” Abstract and Applied Analysis, vol. 2014, pp. 1–13, 2014.
- Shu Xu, Xiang Ling, Carlo Cattani, Gong-Nan Xie, Xiao-Jun Yang, and Yang Zhao, “Local Fractional Laplace Variational Iteration Method for Nonhomogeneous Heat Equations Arising in Fractal Heat Flow,” Mathematical Problems in Engineering, vol. 2014, pp. 1–7, 2014.
- Anupama Choudhary, Devendra Kumar, and Jagdev Singh, “A fractional model of fluid flow through porous media with mean capillary pressure,” Journal of the Association of Arab Universities for Basic and Applied Sciences, 2015.
- H.M. Srivastava, Minjie Luo, and R.K. Raina, “A new integral transform and its applications,” Acta Mathematica Scientia, vol. 35, no. 6, pp. 1386–1400, 2015.
- Seyma Tuluce Demiray, Hasan Bulut, and Fethi Bin Muhammad Belgacem, “Sumudu Transform Method for Analytical Solutions of Fractional Type Ordinary Differential Equations,” Mathematical Problems in Engineering, vol. 2015, pp. 1–6, 2015.
- Ravi Shanker Dubey, Badr Saad T. Alkahtani, and Abdon Atangana, “Analytical Solution of Space-Time Fractional Fokker-Planck Equation by Homotopy Perturbation Sumudu Transform Method,” Mathematical Problems in Engineering, vol. 2015, pp. 1–7, 2015.
- Jagdev Singh, Ram Swroop, and Devendra Kumar, “A computational approach for fractional convection-diffusion equation via integral transforms,” Ain Shams Engineering Journal, 2016.