Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker's Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) equation
Abstract
In this paper, we propose the approximate analytical solutions of conformable time fractional Clannish Random Walker's Parabolic(CRWP) equation and Modified Benjamin-Bona-Mahony(BBM) equation with the aid of generalized homotopy analysis method (q-HAM). The $h$ curves of approximate solutions for both equations are illustrated by graphics to determine the convergence interval. $h$ values obtained from these graphics are used to compare approximate solutions with the analytical solutions. The results show that approximate solutions are consistent with the analytical solutions. Also it is understood that the method is reliable, applicable and efficient technique to get the exact solutions of fractional partial differential equations.
Keywords
References
- [1] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
- [2] A. A. Kilbas , H. M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, 2006.
- [3] K.S. Miller, B. Ross ,An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, 1993.
- [4] R. Khalil, M. A. Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65-70.
- [5] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57-66.
- [6] W.S. Chung, Fractional Newton mechanics with conformable fractional derivative, J. Comput. Appl. Math., 290 (2015), 150-158.
- [7] A. Neirameh, New fractional calculus and application to the fractional-order of extended biological population model, Bol. da Soc. Parana. Matematica, 36(3)(2018), 115.
- [8] N. Benkhettou, S. Hassani, D. F. M. Torres, A conformable fractional calculus on arbitrary time scales, J. King Saud Univ. - Sci., 28(1) (2016), 93-98.
- [9] D. Zhao and T. Li, On conformable delta fractional calculus on time scales, J. Math. Comput. Sci., 16 (2016), 324-335.
- [10] M. Eslami, H. Rezazadeh, The First integral method for Wu-Zhang system with conformable time-fractional derivative, Calcolo, 53(3) (2016), 475-485.
