Solving systems of fractional differential equations by modified fractional differential transform method with adomian polynomials
R. S. Teppawarteppawarrajesh@gmail.comP. G. Department of MathematicsN. E. S. Science CollegeNanded, Maharashtra, 431602, IndiaView full profile → , R. N. Ingleinglerrajkumar22@gmail.comDepartment of MathematicsBahirji Smarak Mahavidyalaya, BasmathnagarHingoli, Maharashtra, 431512, IndiaView full profile → , *R.A. MUNESHWARCorresponding authormuneshwarrajesh10@gmail.comP. G. Department of MathematicsN. E. S. Science CollegeNanded, Maharashtra, 431602, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 12 Jul 2022
- Published Online:
- 27 Feb 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1638
- Pages:
- 17–32
Abstract
Keywords
Subject Classifications
References
[1] I. Podlubny, Fractional Differential Equations, Academic Press, New York (1999).
[2] R.C. Koeller, Applications of fractional calculus to the theory of viscoelasticity, J. Appl. Mech. 51, 299-307 (1984).
[3] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers., Boston, MA (1994).
[4] J.S. Duan, An efficient algorithm for the multivariable Adomian polynomials, Appl. Math. Comput. 217, 2456-2467 (2010).
[5] V. Daftardar-Gejji, H. Jafari, Adomian decomposition: a tool for solving a system of fractional differential equations, J. Math. Anal. Appl. 301, 508-518 (2005).
[6] H. Jafari, V. Daftardar-Gejji, Solving a system of nonlinear fractional differential equations using Adomain decomposition, 196, 644-651 (2006).
[7] S. Momani, N. Shawagfeh, Decomposition method for solving fractional Riccati differential equations, Appl. Math. Comput. 182, 1083-1092 (2006).
[8] I. Hashim, O. Abdulaziz, S. Momani, Homotopy analysis method for fractional IVPs, Commun. Nonlinear Sci. Numer. Simul. 14, 674-684 (2009).
[9] I.H. He, Variational iteration method – a kind of non-linear analytical technique: some examples, Int. J. Non-Linear Mech. 34, 699-08 (1999).
[10] M.M. Khader, Numerical treatment for solving the perturbed fractional PDEs using hybrid techniques, J. Comput. Phys. 250, 565-573 (2013).
[11] N.H. Sweilam, M.M. Khader, A.M. Nagy, Numerical solution of two-sided space-factional wave equation using finite difference method, J. Comput. Appl. Math. 235, 2832-2841 (2011).
[12] J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China, in Chinese (1986).
[13] A. Arikoglu, I. Ozkol, Solution of fractional differential equations by using differential transform method, Chaos Soliton. Fract. 34, 1473-1481 (2007).
[14] V. S. Erturk, S. Momani, Solving system of fractional differential equations using differential transform method, 215, 142-151 (2008).
[15] S.A. Khuri, A Laplace decomposition algorithm applied to class of nonlinear differential equations, J. Math. Appl., 141-155 (2001).
[16] M. Khan, M. Hussain, H. Jafari, Yasir Khan, Application of Laplace decomposition method to solve nonlinear coupled partial differential equations, Word Appl. Sci. J. 9, 13-19 (2010).
[17] H.R. Marasi, N. Sharifi, H. Piri, Modified differental transform method for singular lane Emden Equations in integer and fractional order, TWMS J. App. Eng. Math. V.5, N.1,124-131 (2015).
[18] R.S. Teppawar, R.N. Ingle, S.N. Thorat, Some Results and Applicatios on Conformable Fractional Kamal Transform, Journal of Mathematical and Computational Science, 11(5), 6581-6598 (2021).
[19] J.S. Duan, Recurrence triangle for Adomian polynomials, Appl. Math. Comput. 216,1235-1241 (2010).
[20] K. Shah, H. Khalil, R.A. Khan, Analytical solutions of fractional order diffusion equations by Natural transform method, Iranian J. Sci. Technol. (Trans Sci:A) 42 (3), 1479-1490 (2018).
[21] Elsaid. A., Fractional differential transform method combined with the Adomian polynomials, Apll. Math. Comput., 218, pp. 6899-6911 (2012).
[22] L. Ghaffour, Z. Dahmani: Fractional differential equations with arbitrary singularities, Journal of Information and Optimization Sciences, 39 (7), pp. 1547-1565 (2018).
[23] Kilbas, H. Srivastava J. Trujillo: Theory and Applications of Fractional Differential Equations in Math Studies, North-Holland, New York (2006).
[24] Millar K. S.: An Introduction to Fractional Calculus and Fractional Differential Equations, J Wiley and sons New York (1993).
[25] Caputo M. Linear models of dissipation whose Q is almost frequency independent. Part II. J Roy Austral Soc; 13 : 529-39 (1967).




