Analytical Approach to Solving Fractional Partial Differential Equation by Optimal q-Homotopy Analysis Method

被引:6
作者
Darzi R. [1 ]
Agheli B. [2 ]
机构
[1] Department of Mathematics, Neka Branch, Islamic Azad University, Neka
[2] Department ofMathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr
关键词
Caputo derivative; nonlinear fractional partial differential equation; optimal q-homotopy analysis method;
D O I
10.1134/S1995423918020040
中图分类号
O172 [微积分];
学科分类号
摘要
The optimal q-homotopy analysis method is employed in order to solve partial differential equations (PDEs) featuring a time-fractional derivative. To illustrate the simplicity and ability of the suggested approach, some specific and clear examples are given. All numerical calculations in this manuscript have been carried out withMathematica package. © 2018, Pleiades Publishing, Ltd.
引用
收藏
页码:134 / 145
页数:11
相关论文
共 20 条
[1]  
Liao S.J., The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems, (1992)
[2]  
El-Tawil M.A., Huseen S.N., The q-Homotopy Analysis Method (q-HAM), Int. J. Appl.Math. Mech., 8, 15, pp. 51-75, (2012)
[3]  
Huseen S.N., Grace S.R., El-Tawil M.A., The Optimal q-Homotopy Analysis Method (Oq-HAM), Int. J. Comp. Technol., 11, 8, pp. 2859-2866, (2012)
[4]  
Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, (2006)
[5]  
Miller K.S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations, (1993)
[6]  
Momani S., Shawagfeh N., Decomposition Method for Solving Fractional Riccati Differential Equations, Appl.Math. Comput., 182, pp. 1083-1092, (2006)
[7]  
Wang Q., Numerical Solutions for Fractional KdV–Burgers Equation by Adomian DecompositionMethod, Appl.Math. Comp., 182, pp. 1048-1055, (2006)
[8]  
Inc M., The Approximate and Exact Solutions of the Space-and Time-Fractional Burgers Equations with Initial Conditions by Variational Iteration Method, J. Math. An. Appl., 345, pp. 476-484, (2008)
[9]  
Yang X.J., Baleanu D., Khan Y., Mohyud-Din S.T., Local Fractional Variational Iteration Method for Diffusion andWave Equations on Cantor Sets, Rom. J. Phys., 59, pp. 36-48, (2014)
[10]  
Momani S., Odibat Z., Homotopy Perturbation Method for Nonlinear Partial Differential Equations of Fractional Order, Phys. Lett. A, 365, pp. 345-350, (2007)