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Existence of positive solutions for the nonlinear fractional differential equation D s u(x) = f (x, u(x)), 0 < s < 1, has been studied (S. Zhang, J. Math. Anal. Appl. 252 (2000) 804–812), where D s denotes Riemann–Liouville fractional derivative. In the present work we study existence of positive solutions in case of the nonlinear fractional differential… (More)
Adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations: (k) i (0) = c i k , 0 k [ i ], 1 i n and D i denotes Caputo fractional derivative. Some examples are solved as illustrations, using symbolic computation.
Adams-Bashforth-Moulton algorithm has been extended to solve delay differential equations of fractional order. Numerical illustrations are presented to demonstrate utility of the method. Chaotic behaviour is observed in one dimensional delayed systems of fractional order. We further find the smallest fractional order for the chaotic behaviour. It is also… (More)