A novel numerical technique used in the solution of ordinary differential equations with a mixture of integer and fractional derivatives

Details A novel numerical technique used in the solution of ordinary differential equations with a mixture of integer and fractional derivatives A novel numerical technique used in the solution of ordinary differential equations with a mixture of integer and fractional derivatives

2007-12-02

arxiv.org/abs/0712.0168v1

Mathematics

Numerical Analysis

31 pages, 6 figures, 6 tables. This manuscript was sent to the Journal of Numerical Algorithms

Scientific paper

Using both fractional derivatives, defined in the Riemann-Liouville and Caputo senses, and classical derivatives of the integer order we examine different numerical approaches to ordinary differential equations. Generally we formulate some algorithms where four discrete forms of the Caputo derivative and three different numerical techniques of solving ordinary differential equations are proposed. We then illustrate how to introduce classical initial conditions into equations where the Riemann-Liouville derivative is included.

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