Abstract
In this paper we propose the collocation method to achieve the numerical solution of fractional order linearsystems where a Fractional Derivative is defined in the Caputo sense.We use Taylor collocation method,which is based on collocation method for solving fractional differential equation. This method is based onfirst taking the truncated Taylor expansions of the vector function’s solution in the Fractional order linearsystem and then substituting their matrix forms into the system. Using collocation points, we have a systemof linear algebraic equation.The method has been tested by some numerical examples.DOI : http://dx.doi.org/10.22342/jims.23.1.257.
Highlights
Fractional differential equations have been generalized from integer order derivatives through replacing the integer order derivatives by fractional ones
We present a numerical solution of the fractional order system through the use of Taylor collocation method for a system of the form aDtαx(t) = Ax(t) + Bu(t) y(t) = Cx(t) + Du(t), (3)
In this paper we presented a collocation method to solve fractional order linear system with initial conditions
Summary
And in this part of the study, we deal with fractional calculus, definitions and theorems; see [23, 14, 17]. for more details in this regard. And in this part of the study, we deal with fractional calculus, definitions and theorems; see [23, 14, 17]. The Riemann-Liouville fractional derivative of order α with respect to the variable x and with the starting point at x = a is aDtαf (x) =. The fractional derivative of f (x) in the Caputo form is defined as. (Fractional Derivative of a Vector) If X(x) = (X1(x) · · · Xn(x))T is a vector function, we define. Two following theorems show the form of the general solution of (9) where Eα(t) is the MittagLeffler function. For the inhomogeneous boundary value problem, we have the following theorem. Following we recall the generalization of Taylor formula which forms the basis of our numerical method.
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