Recursive-operational method for fractional systems
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Gabriel Bengochea
Abstract
In this chapter we present a recursive-operational method for studying fractional continuous-time linear systems. The approach that we follow is an algebraic version of the usual convolution product. With it, we are able to compute the output of fractional linear systems. The method is recursive in the sense that we can add or remove (pseudo-) poles or zeros individually. The performance and accuracy of the method are illustrated by numerical examples. The procedure can be used also in nonlinear systems. To illustrate this feature we solve the fractional version of the logistic equation.
Abstract
In this chapter we present a recursive-operational method for studying fractional continuous-time linear systems. The approach that we follow is an algebraic version of the usual convolution product. With it, we are able to compute the output of fractional linear systems. The method is recursive in the sense that we can add or remove (pseudo-) poles or zeros individually. The performance and accuracy of the method are illustrated by numerical examples. The procedure can be used also in nonlinear systems. To illustrate this feature we solve the fractional version of the logistic equation.
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Economic models with power-law memory 1
- Four-quadrant fractors and their applications in fractional order circuits 33
- Energy harvesting in dynamical systems with fractional-order physical properties 63
- Fractional kinetics of charge carriers in supercapacitors 87
- Recursive-operational method for fractional systems 119
- Discrete-time fractional signals and systems 149
- Signal prediction using fractional derivative models 179
- Spectral methods within fractional calculus 207
- Design and generation of fractional-order multi-scroll chaotic attractors 233
- Discrete fractional masks and their applications to image enhancement 261
- Existence theory for fractional differential equations with nonlocal integro-multipoint boundary conditions with applications 271
- Index 283
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Economic models with power-law memory 1
- Four-quadrant fractors and their applications in fractional order circuits 33
- Energy harvesting in dynamical systems with fractional-order physical properties 63
- Fractional kinetics of charge carriers in supercapacitors 87
- Recursive-operational method for fractional systems 119
- Discrete-time fractional signals and systems 149
- Signal prediction using fractional derivative models 179
- Spectral methods within fractional calculus 207
- Design and generation of fractional-order multi-scroll chaotic attractors 233
- Discrete fractional masks and their applications to image enhancement 261
- Existence theory for fractional differential equations with nonlocal integro-multipoint boundary conditions with applications 271
- Index 283
