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Lie symmetry analysis of conformable differential equations

1 Équipe Modélisation Mathématique et Calcul Scientifiques, Département de Mathématiques, École Nationale Supérieure des Arts et Métiers, Université Moulay Ismaïl, Meknès, Morocco
2 Centre Régional des Métiers de l’ Éducation et de la Formation, Fès-Meknès, Morocco

Special Issues: Initial and Boundary Value Problems for Differential Equations

In this paper, we construct a proper extension of the classical prolongation formula of point transformations for conformable derivative. This technique is illustrated and employed to construct a symmetry group admitted by a conformable ordinary and partial differential equations. Using Lie symmetry analysis, we obtain an exact solution of the conformable heat equation.
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Keywords conformable derivative; fractional differential equations; Lie symmetry; conformable heat equation

Citation: Youness Chatibi, El Hassan El Kinani, Abdelaziz Ouhadan. Lie symmetry analysis of conformable differential equations. AIMS Mathematics, 2019, 4(4): 1133-1144. doi: 10.3934/math.2019.4.1133


  • 1. S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Yverdon: Gordon and Breach Science Publishers, 1993.
  • 2. M. Dalir and M. Bashour, Applications of fractional calculus, Appl. Math. Sci., 4 (2010), 1021-1032.
  • 3. R. Hilfer, Applications of Fractional Calculus in Physics, Singapore: Word Scientific, 2000.
  • 4. I. Podlubny, Fractional Differential Equations, New York: Academic Press, 1999.
  • 5. R. Khalil, M. A. Horani, A. Yousef, et al. A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65-70.    
  • 6. T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57-66.    
  • 7. D. Zhao and M. Luo, General conformable fractional derivative and its physical interpretation, Calcolo, 54 (2017), 903-917.    
  • 8. J. H. He, Homotopy perturbation method: A new nonlinear analytical technique, Appl. Math. Comput., 135 (2003), 73-79.
  • 9. F. Tchier, M. Inc and A. Yusuf, Symmetry analysis, exact solutions and numerical approximations for the space-time Carleman equation in nonlinear dynamical systems, Eur. Phys. J. Plus, 134 (2019), 1-18.    
  • 10. A. Yusuf, M. Inc and M. Bayram, Soliton solutions for Kudryashov-Sinelshchikov equation, Sigma J. Eng. Nat. Sci., 37 (2019), 439-444.
  • 11. M. Inc, A. Yusuf, A. I. Aliyu, et al. Dark and singular optical solitons for the conformable space-time nonlinear Schrödinger equation with Kerr and power law nonlinearity, Optik, 162 (2018), 65-75.    
  • 12. M. Inc, A. Yusuf, A. I. Aliyu, et al. Lie symmetry analysis and explicit solutions for the time fractional generalized Burgers-Huxley equation, Opt. Quant. Electron., 50 (2018), 1-16.    
  • 13. A. Akgül, Reproducing kernel method for fractional derivative with non-local and non-singular kernel, In: Fractional Derivatives with Mittag-Leffler Kernel, Series of Studies in Systems, Decision and Control, Springer, Cham, 194 (2019), 1-12.
  • 14. A. Akgül, A novel method for a fractional derivative with non-local and non-singular kernel, Chaos Soliton Fractals, 114 (2018), 478-482.    
  • 15. M. G. Sakar, O. Saldir and A. Akgül, A Novel Technique for Fractional Bagley-Torvik Equation, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., (2018), 1-7.
  • 16. M. Modanli and A. Akgül, Numerical solution of fractional telegraph differential equations by theta-method, Eur. Phys. J. Spec. Top., 226 (2017), 3693-3703.    
  • 17. E. K. Akgül, Solutions of the linear and nonlinear differential equations within the generalized fractional derivatives, Chaos, 29 (2019), Article ID 023108.
  • 18. E. K. Akgül, B. Orcan and A. Akgül, Solving higher-order fractional differential equations by reproducing kernel Hilbert space method, J. Adv. Phys., 7 (2018), 98-102.    
  • 19. N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, Volume I: Symmetries, Exact Solutions, and Conservation Laws, CRC Press, Boca Raton, FL, 1994.
  • 20. N. H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, Wiley, Chichester, 1999.
  • 21. P. J. Olver, Application of Lie Groups to Differential Equation, Springer, 1986.
  • 22. G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Cambridge Texts in Applied Mathematics, Springer, 1989.
  • 23. R. K. Gazizov, A. A. Kasatkin and S. Y. Lukashchuk, Continuous transformation groups of fractional differential equations, Vestnik USATU, 9 (2007), 125-135.
  • 24. E. H. El Kinani and A. Ouhadan, Exact solutions of time fractional Kolmogorov equation by using Lie symmetry analysis, J. Fract. Calc. Appl., 5 (2014), 97-104.
  • 25. A. Ouhadan and E. H. El Kinani, Lie symmetry analysis of some time fractional partial differential equations, Int. J. Mod. Phys. Conf. Ser., 38 (2015), Article ID 1560075.
  • 26. T. Bakkyaraj and R. Sahadevan, Group formalism of Lie transformations to time-fractional partial differential equations, Pramana J. Phys., 85 (2015), 849-860.    
  • 27. T. Bakkyaraj and R. Sahadevan, Invariant analysis of nonlinear fractional ordinary differential equations with Riemann-Liouville fractional derivative, Nonlinear Dyn., 80 (2015), 447-455.    


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