Application of the Lie Symmetry Analysis for second-order fractional differential equations

Iranian Journal of Optimization

مقاله 8، دوره 9، شماره 2، اسفند 2017، صفحه 79-83   

نوع مقاله: Research Paper

نویسندگان

Mousa Ilie¹؛ Jafar Biazar^{* 2}؛ Zainab Ayati³

¹Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.

²Department of Mathematics, Faculty of Science, University of Guilan

³Department of Engineering sciences, Faculty of Technology and Engineering East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran

چکیده

Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to illustrate the proposed approach.

کلیدواژه‌ها

fractional differential equations؛ Lie Symmetry method؛ conformable fractional derivative

مراجع

Abdeljawad, T. (2015). On conformable fractional calculus. Journal of computational and Applied Mathematics, 279, 57-66.

 Arrigo, D. J. (2015). Symmetry analysis of differential equations: an introduction. John Wiley & Sons.

Elsaid, A., Abdel Latif., M. S., & Maneea, M.(2016).  Similarity solutions for solving Riesz fractional partial differential equations, Progr. Fract. Differ. 2(4) 293-298.

Gaur, M., & Singh, K. (2016). Symmetry analysis of time fractional-potential Burgers' equation. Mathematical Communications, 1-11.

 Gaur, M., & Singh, K. (2016). Symmetry Classification and Exact Solutions of a Variable Coefficient Space-Time Fractional Potential Burgers’ Equation. International Journal of Differential Equations, 2016.

Hydon, P. E., & Hydon, P. E. (2000). Symmetry methods for differential equations: a beginner's guide (Vol. 22). Cambridge University Press.

Khalil, H., Khan, R., & Rashidi, M. M. (2015). Brenstien polynomials and its application to fractional differential equation. Computational methods for differential equations, 3(1), 14-35.

 Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65-70.

Kumar, S., Kumar, D., Abbasbandy, S., & Rashidi, M. M. (2014). Analytical solution of fractional Navier–Stokes equation by using modified Laplace decomposition method. Ain Shams Engineering Journal, 5(2), 569-574.

Olver, P. J. (2000). Applications of Lie groups to differential equations (Vol. 107). Springer Science & Business Media.

 Ouhadan, A., & EL KINANI, E. H. (2014). Exact solutions of time fractional Kolmogorov equation by using Lie symmetry analysis. Journal of Fractional Calculus and Applications, 5(1), 97-104.

Singh, J., Rashidi, M. M., Kumar, D., & Swroop, R. (2016). A fractional model of a dynamical Brusselator reaction-diffusion system arising in triple collision and enzymatic reactions. Nonlinear Engineering, 5(4), 277-285

Yang, A. M., Zhang, Y. Z., Cattani, C., Xie, G. N., Rashidi, M. M., Zhou, Y. J., & Yang, X. J. (2014, March). Application of local fractional series expansion method to solve Klein-Gordon equations on Cantor sets. In Abstract and Applied Analysis (Vol. 2014). Hindawi Publishing Corporation.

Zhanglie, Y. (2015). Symmetry analysis to general time-fractional Korteweg-De Vries equations, Fractional Differential Calculus,  5,(2),  125-133.