Neamaty, A., Agheli, B., Darzi, R. (2013). New Integral Transform for Solving Nonlinear Partial Di erential Equations of fractional order. Theory of Approximation and Applications, 10(1), 69-86.
A. Neamaty; B. Agheli; R. Darzi. "New Integral Transform for Solving Nonlinear Partial Di erential Equations of fractional order". Theory of Approximation and Applications, 10, 1, 2013, 69-86.
Neamaty, A., Agheli, B., Darzi, R. (2013). 'New Integral Transform for Solving Nonlinear Partial Di erential Equations of fractional order', Theory of Approximation and Applications, 10(1), pp. 69-86.
Neamaty, A., Agheli, B., Darzi, R. New Integral Transform for Solving Nonlinear Partial Di erential Equations of fractional order. Theory of Approximation and Applications, 2013; 10(1): 69-86.
New Integral Transform for Solving Nonlinear Partial Di erential Equations of fractional order
1Department of Mathematics, University of Mazandaran, Babolsar, Iran
2Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
3Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran
Abstract
In this work, we have applied Elzaki transform and He's homotopy perturbation method to solve partial di erential equation (PDEs) with time-fractional derivative. With help He's homotopy per- turbation, we can handle the nonlinear terms. Further, we have applied this suggested He's homotopy perturbation method in order to reformulate initial value problem. Some illustrative examples are given in order to show the ability and simplicity of the approach. All numerical calculations in this manuscript were performed on a PC applying some programs written in Maple.
Article Title [Persian]
New Integral Transform for Solving
Nonlinear Partial Di erential Equations of
fractional order
Authors [Persian]
A. Neamaty1; B. Agheli2; R. Darzi3
1Department of Mathematics, University of Mazandaran, Babolsar, Iran
2Department of Mathematics, Qaemshahr Branch, Islamic Azad University,
Qaemshahr, Iran
3Department of Mathematics, Neka Branch, Islamic Azad University, Neka,
Iran
Abstract [Persian]
In this work, we have applied Elzaki transform and He's homotopy perturbation method to solve partial di erential equation (PDEs) with time-fractional derivative. With help He's homotopy per- turbation, we can handle the nonlinear terms. Further, we have applied this suggested He's homotopy perturbation method in order to reformulate initial value problem. Some illustrative examples are given in order to show the ability and simplicity of the approach. All numerical calculations in this manuscript were performed on a PC applying some programs written in Maple.
[1] J.H. He, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178 (3-4) (1999), pp. 257{262. [2] E. Babolian, A. Azizi, J. Saeidian , Some notes on using the homotopy perturbation method for solving time-dependent di erential equations, Mathematical and Computer Modelling, 50 ( 2009), pp. 213{224. [3] S. Abbasbandy, Iterated He's homotopy perturbation method for quadratic Riccati di erential equation, Journal of Computational and Applied Mathematics, 175 (2006), pp. 581{589. [4] Z. Odibat, Shaher Momani, The variational iteration method: an ecient scheme for handling fractional partial di erential equations in uid mechanics, Computers and Mathematics with Applications, 58 (2009), pp. 2199{2208. [5] G.M. Mophou, Existence and uniqueness of mild solutions to impulsive fractional di erential equations, Nonlinear Analysis: Theory, Methods and Applications, 72 (2010), pp. 1604{1615. [6] F. Huang, F. Liu, The time fractional di usion and fractional advection- dispersion equation, ANZIAM, 46 (2005), pp. 1{14. [7] D. Taka^ci, A. Taka^ci, M.^Strboja, On the character of operational solutions of the time-fractional di usion equation, Nonlinear Analysis: Theory, Methods and Applications, 72 (2010), pp. 2367{2374.
[8] C. Xue, J. Nie, W. Tan, An exact solution of start-up ow for the fractional generalized Burgers' uid in a porous half-space, Nonlinear Analysis: Theory, Methods and Applications, 69 (2008), pp. 2086{2094. [9] S. Guo, L. Mei, Y. Fang, Z. Qiu, Compacton and solitary pattern solutions for nonlinear dispersive KdV-type equations involving Jumarie's fractional derivative, Physics Letters A, 376 (2012), pp. 158{164. [10] S. Guo, L. Mei, Y. Ling, Y. Sun, The improved fractional sub-equation method and its applications to the space-time fractional di erential equations in uid mechanics, Physics Letters A, 376 (2012), pp. 407{411. [11] Y. Liu, Variational homotopy perturbation method for solving fractional initial boundary value problems, Abstract and Applied Analysis, 2012 (2012), http://dx.doi.org/10.1155/2012/727031. [12] T. M. Elzaki and S. M. Elzaki, Application of New Transform "Elzaki Transform" to Partial Di erential Equations, Global Journal of Pure and Applied Mathematics, 1 (2011), pp. 65{70. [13] J. Zhang, A Sumudu based algorithm for solving di erential equations, Computational Science Journal Moldova, 15(3), pp. 303 { 313. [14] H. Eltayeb and A. kilicman, A Note on the Sumudu Transforms and di erential Equations, Applied Mathematical Sciences, 4 (2010), pp. 1089{ 1098. [15] T. Elzaki, S. M. Elzaki, and E. M. A. Hilal, Elzaki and Sumudu Transforms for Solving Some Di erential Equations, Global Journal of Pure and Applied Mathematics, 8 (2012), pp. 167{173. [16] I. Podlubny, Fractional di erential equations, Academic Press, San Diego, CA, (1999). [17] Tarig M. Elzaki, Salih M. Elzaki, and Eman M. A. Hilal, Elzaki and Sumudu Transforms for Solving Some Di erential Equations, Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Volume 8, Number., 2 (2012), pp. 167{173. [18] Z. Odibat, S. Momani, Numerical methods for nonlinear partial di erential equations of fractional order, Applied Mathematical Modelling, 32 (2008), pp. 28{39.
Top