Journal of applied mathematics & informatics
- Volume 23 Issue 1_2
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- Pages.229-241
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- 2007
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- 2734-1194(pISSN)
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- 2234-8417(eISSN)
NUMERICAL SIMULATION OF THE FRACTIONAL-ORDER CONTROL SYSTEM
Abstract
Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of the such controllers for the more efficient control of fractional-order dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into equivalent a system of equations. The existence and uniqueness of the new system are proved. A fractional order difference approximation is constructed by a decoupled technique and fractional-order numerical techniques. The consistence, convergence and stability of the numerical approximation are proved. Finally, some numerical results are presented to demonstrate that the numerical approximation is a computationally efficient method. The new method can be applied to solve the fractional-order control system.
Keywords
- Multi-term;
- fractional control system;
- Caputo derivative;
- numerical approximation;
- consistence;
- convergence;
- stability