ANALYTICAL SOLUTION FOR MULTI-TERM FRACTIONAL DELAY DIFFERENTIAL EQUATIONS
E. A. A. ZIADA *
Department of Basic Science, Nile Higher Institute for Engineering & Technology, Mansoura, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this paper a nonlinear delay differential equation (NDDE) of arbitrary orders of Riemann- Liouville sense is studied. Adomian decomposition method (ADM) is used to solve this type of equations. The existence and stability of a unique solution will be proved. Convergence analysis of ADM is discussed. The maximum absolute truncated error of Adomian’s series solution is estimated. Stability of the solution is also discussed.
Keywords: Nonlinear delay differential equation, arbitrary orders, banach space, fixed point theorem, convergence analysis, stability, adomian decomposition method