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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 279681, 8 pages
A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions
1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Yildiz Technical University, Department of Mathematical Engineering, Davutpasa, 34210 İstanbul, Turkey
Received 10 January 2013; Accepted 1 March 2013
Academic Editor: Mustafa Bayram
Copyright © 2013 Abdon Atangana and Aydin Secer. 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 [36 citations]
The following is the list of published articles that have cited the current article.
- G.F. Jefferson, and J. Carminati, “FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations,” Computer Physics Communications, 2013.
- Abdon Atangana, and Ernestine Alabaraoye, “Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4(+) cells and attractor one-dimensional Keller-Segel equations,” Advances In Difference Equations, 2013.
- Zuodong Yang, “Analytic Solution of a Class of Fractional Differential Equations,” Abstract and Applied Analysis, 2013.
- Abdon Atangana, and Dumitru Baleanu, “Nonlinear Fractional Jaulent-Miodek and Whitham-Broer-Kaup Equations within Sumudu Transform,” Abstract and Applied Analysis, vol. 2013, pp. 1–8, 2013.
- Manuel A. Duarte-Mermoud, Norelys Aguila-Camacho, and Javier A. Gallegos, “Sufficient Condition on the Fractional Integral for the Convergence of a Function,” Scientific World Journal, 2013.
- Daliang Zhao, and Yansheng Liu, “Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems,” The Scientific World Journal, vol. 2013, pp. 1–9, 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.
- Abdon Atangana, and Necdet Bildik, “Approximate Solution of Tuberculosis Disease Population Dynamics Model,” Abstract and Applied Analysis, vol. 2013, pp. 1–8, 2013.
- Abdon Atangana, and Dumitru Baleanu, “Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes,” Abstract and Applied Analysis, vol. 2013, pp. 1–8, 2013.
- Abdon Atangana, and Necdet Bildik, “Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind,” Mathematical Problems in Engineering, vol. 2013, pp. 1–11, 2013.
- Pengde Wang, and Chengming Huang, “A conservative linearized difference scheme for the nonlinear fractional Schrödinger equation,” Numerical Algorithms, 2014.
- V. Kobelev, “Some Basic Solutions for Nonlinear Creep,” International Journal of Solids and Structures, 2014.
- Abdon Atangana, and Dumitru Baleanu, “Modelling the advancement of the impurities and the melted oxygen concentration within the scope of fractional calculus,” International Journal Of Non-Linear Mechanics, vol. 67, pp. 278–284, 2014.
- Abdon Atangana, and Emile Franc Doungmo Goufo, “Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems,” Mathematical Problems in Engineering, vol. 2014, pp. 1–7, 2014.
- Abdon Atangana, and Innocent Rusagara, “On the Agaciro Equation via the Scope of Green Function,” Mathematical Problems in Engineering, vol. 2014, pp. 1–8, 2014.
- Abdon Atangana, and Suares Clovis Oukouomi Noutchie, “On Multi-Laplace Transform for Solving Nonlinear Partial Differential Equations with Mixed Derivatives,” Mathematical Problems in Engineering, vol. 2014, pp. 1–9, 2014.
- Abdon Atangana, and Suares Clovis Oukouomi Noutchie, “Modelling the Formation of Liver Zones within the Scope of Fractional Order Derivative,” BioMed Research International, vol. 2014, pp. 1–10, 2014.
- Abdon Atangana, Seyma Tuluce Demiray, and Hasan Bulut, “Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014.
- Abdon Atangana, “On the Singular Perturbations for Fractional Differential Equation,” The Scientific World Journal, vol. 2014, pp. 1–9, 2014.
- Guang-Sheng Chen, H. M. Srivastava, Pin Wang, and Wei Wei, “Some Further Generalizations of Hölder's Inequality and Related Results on Fractal Space,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014.
- José Gómez-Aguilar, Huitzilin Yépez-Martínez, Celia Calderón-Ramón, Irene Cruz-Orduña, Ricardo Escobar-Jiménez, and Victor Olivares-Peregrino, “Modeling of a Mass-Spring-Damper System by Fractional Derivatives with and without a Singular Kernel,” Entropy, vol. 17, no. 9, pp. 6289–6303, 2015.
- Emile Franc, and Doungmo Goufo, “A Biomathematical View On The Fractional Dynamics Of Cellulose Degradation,” Fractional Calculus And Applied Analysis, vol. 18, no. 3, pp. 554–564, 2015.
- Larisse Bolton, Alain H. J. J. Cloot, Schalk W. Schoombie, and Jacobus P. Slabbert, “A proposed fractional-order Gompertz model and its application to tumour growth data,” Mathematical Medicine And Biology-A Journal Of The Ima, vol. 32, no. 2, pp. 187–207, 2015.
- Abdon Atangana, “Modeling the Enzyme Kinetic Reaction,” Acta Biotheoretica, 2015.
- Tridip Sardar, Sourav Rana, and Joydev Chattopadhyay, “A mathematical model of dengue transmission with memory,” Communications In Nonlinear Science And Numerical Simulation, vol. 22, no. 1-3, pp. 511–525, 2015.
- Ram Saxena, Zivorad Tomovski, and Trifce Sandev, “Analytical Solution of Generalized Space-Time Fractional Cable Equation,” Mathematics, vol. 3, no. 2, pp. 153–170, 2015.
- Abdon Atangana, Dumitru Baleanu, and Ahmed Alsaedi, “New properties of conformable derivative,” Open Mathematics, vol. 13, pp. 889–898, 2015.
- Jianping Zhang, and Ke Chen, “A Total Fractional-Order Variation Model for Image Restoration with Nonhomogeneous Boundary Conditions and Its Numerical Solution,” SIAM Journal on Imaging Sciences, vol. 8, no. 4, pp. 2487–2518, 2015.
- Abdon Atangana, and Juan Jose Nieto, “Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel,” Advances in Mechanical Engineering, vol. 7, no. 10, 2015.
- Ali H. Bhrawy, Dumitru Baleanu, and Fouad Mallawi, “A New Numerical Technique For Solving Fractional Sub-Diffusion And Reaction Sub-Diffusion Equations With A Non-Linear Source Term,” Thermal Science, vol. 19, pp. S25–S34, 2015.
- Abdon Atangana, and Emile Franc Doungmo Goufo, “Solution Of Diffusion Equation With Local Derivative With New Parameter,” Thermal Science, vol. 19, pp. S231–S238, 2015.
- Emile Franc Doungmo Goufo, and Stella Mugisha, “On Analysis of Fractional Navier-Stokes Equations via Nonsingular Solutions and Approximation,” Mathematical Problems in Engineering, vol. 2015, pp. 1–8, 2015.
- Sertan Alkan, and Aydin Secer, “Application of Sinc-Galerkin Method for Solving Space-Fractional Boundary Value Problems,” Mathematical Problems in Engineering, vol. 2015, pp. 1–10, 2015.
- Victor Fabian Morales-Delgado, José Francisco Gómez-Aguilar, Huitzilin Yépez-Martínez, Dumitru Baleanu, Ricardo Fabricio Escobar-Jimenez, and Victor Hugo Olivares-Peregrino, “Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular,” Advances in Difference Equations, vol. 2016, no. 1, 2016.
- J.F. Gómez-Aguilar, H. Yépez-Martínez, R.F. Escobar-Jiménez, C.M. Astorga-Zaragoza, and J. Reyes-Reyes, “Analytical and numerical solutions of electrical circuits described by fractional derivatives,” Applied Mathematical Modelling, 2016.
- Abdon Atangana, “Exact solution of the time-fractional groundwater flow equation within a leaky aquifer equation,” Journal Of Vibration And Control, vol. 22, no. 7, pp. 1749–1756, 2016.