Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations
Applied Numerical Mathematics
On accurate product integration rules for linear fractional differential equations
Journal of Computational and Applied Mathematics
Evolutionary computational intelligence in solving the fractional differential equations
ACIIDS'10 Proceedings of the Second international conference on Intelligent information and database systems: Part I
Fractional Bloch equation with delay
Computers & Mathematics with Applications
Numerical approaches to fractional calculus and fractional ordinary differential equation
Journal of Computational Physics
Computers & Mathematics with Applications
Analytical solution of the linear fractional system of commensurate order
Computers & Mathematics with Applications
| Hi-index | 0.09 |
The generalized Adams-Bashforth-Moulton method, often simply called ''the fractional Adams method'', is a useful numerical algorithm for solving a fractional ordinary differential equation: D"*^@ay(t)=f(t,y(t)),y^(^k^)(0)=y"0^(^k^),k=0,1,...,n-1, where @a0,n=@?@a@? is the first integer not less than @a, and D"*^@ay(t) is the @ath-order fractional derivative of y(t) in the Caputo sense. Although error analyses for this fractional Adams method have been given for (a) 01, y@?C^1^+^@?^@a^@?[0,T], (c) 01, f@?C^3(G), there are still some unsolved problems-(i) the error estimates for @a@?(0,1), f@?C^3(G), (ii) the error estimates for @a@?(0,1), f@?C^2(G), (iii) the solution y(t) having some special forms. In this paper, we mainly study the error analyses of the fractional Adams method for the fractional ordinary differential equations for the three cases (i)-(iii). Numerical simulations are also included which are in line with the theoretical analysis.