Modern control theory (3rd ed.)
Modern control theory (3rd ed.)
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
An approximate method for numerical solution of fractional differential equations
Signal Processing - Fractional calculus applications in signals and systems
Numerical approach to differential equations of fractional order
Journal of Computational and Applied Mathematics
Solving systems of fractional differential equations using differential transform method
Journal of Computational and Applied Mathematics
Analytical solution of the linear fractional differential equation by Adomian decomposition method
Journal of Computational and Applied Mathematics
A new analytical approximate method for the solution of fractional differential equations
International Journal of Computer Mathematics
Computational algorithms for computing the fractional derivatives of functions
Mathematics and Computers in Simulation
Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering
Functional Fractional Calculus for System Identification and Controls
Functional Fractional Calculus for System Identification and Controls
On the fractional Adams method
Computers & Mathematics with Applications
Random-order fractional differential equation models
Signal Processing
Numerical approaches to fractional calculus and fractional ordinary differential equation
Journal of Computational Physics
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A useful representation of fractional order systems is the state space representation. For the linear fractional systems of commensurate order, the state space representation is defined as for regular integer state space representation with the state vector differentiated to a real order. This paper presents a solution of the linear fractional order systems of commensurate order in the state space. The solution is obtained using a technique based on functions of square matrices and the Cayley-Hamilton theorem. The technique developed for linear systems of integer order is extended to derive analytical solutions of linear fractional systems of commensurate order. The basic ideas and the derived formulations of the technique are presented. Both, homogeneous and inhomogeneous cases with usual input functions are solved. The solution is calculated in the form of a linear combination of suitable fundamental functions. The presented results are illustrated by analyzing some examples to demonstrate the effectiveness of the presented analytical approach.