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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)

- Hossein Jafari, Varsha Daftardar-Gejji
- Applied Mathematics and Computation
- 2006

- Hossein Jafari, Varsha Daftardar-Gejji
- Applied Mathematics and Computation
- 2006

- Varsha Daftardar-Gejji, Sachin Bhalekar
- Applied Mathematics and Computation
- 2008

- Sachin Bhalekar, Varsha Daftardar-Gejji
- Applied Mathematics and Computation
- 2008

In the present article, we implement the new iterative method (NIM) proposed by Daftardar-Gejji and Jafari [V. Daftardar-Gejji, H. Jafari, An iterative method for solving non linear functional equations, J. Math. Anal. Appl. 316 (2006) 753–763] to solve linear/nonlinear partial differential equations of integer and fractional order. The results obtained are… (More)

- Hossein Jafari, Varsha Daftardar-Gejji
- Applied Mathematics and Computation
- 2006

- Varsha Daftardar-Gejji, Hossein Jafari
- Applied Mathematics and Computation
- 2007

Adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations: D i yi (x)=Ni(x, y1, . . . , yn), y i (0)= c k, 0 k [ i ], 1 i n and D i denotes Caputo fractional derivative. Some examples are solved as illustrations, using symbolic computation. © 2005 Elsevier B.V. All rights reserved.

- Sachin Bhalekar, Varsha Daftardar-Gejji, Dumitru Baleanu, Richard L. Magin
- Computers & Mathematics with Applications
- 2011

In the present paper we discuss the existence of positive solutions in the case of multi-term non-autonomous fractional differential equations with polynomial coefficients; the constant coefficient case has been studied in [2]. We consider the equation “ Dn − n−1 X j=1 pj(x)D αn−j ” y = f(x, y). We state various conditions on f and pj ’s under which this… (More)