In this paper, we apply the Adomian decomposition method (ADM) for solving linear and nonlinear fractional differential equations (FDEs). The existence and uniqueness of the solution are proved. The convergence of the series solution and the error analysis are discussed. Some applications are solved such as relaxation-oscillation equation, Basset problem and fractional Riccati differential equation.
Ziada, E. (2021). Analytical solution of linear and nonlinear fractional differential equations. Nile Journal of Basic Science, 1(1), 1-13. doi: 10.21608/njbs.2021.202511
MLA
Eman A. A. Ziada. "Analytical solution of linear and nonlinear fractional differential equations". Nile Journal of Basic Science, 1, 1, 2021, 1-13. doi: 10.21608/njbs.2021.202511
HARVARD
Ziada, E. (2021). 'Analytical solution of linear and nonlinear fractional differential equations', Nile Journal of Basic Science, 1(1), pp. 1-13. doi: 10.21608/njbs.2021.202511
VANCOUVER
Ziada, E. Analytical solution of linear and nonlinear fractional differential equations. Nile Journal of Basic Science, 2021; 1(1): 1-13. doi: 10.21608/njbs.2021.202511