The General Solution of Singular Fractional-Order Linear Time-Invariant Continuous Systems with Regular Pencils

This paper introduces a general solution of singular fractional-order linear-time invariant (FoLTI) continuous systems using the Adomian Decomposition Method (ADM) based on the Caputo's definition of the fractional-order derivative. The complexity of their entropy lies in defining the complete...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2018-05, Vol.20 (6), p.400
Main Authors: Batiha, Iqbal, El-Khazali, Reyad, AlSaedi, Ahmed, Momani, Shaher
Format: Article
Language:English
Subjects:
Adomian decomposition
descriptor fractional linear systems
fractional calculus
Mittag–Leffler function
regular pencils
Schur factorization
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Summary:This paper introduces a general solution of singular fractional-order linear-time invariant (FoLTI) continuous systems using the Adomian Decomposition Method (ADM) based on the Caputo's definition of the fractional-order derivative. The complexity of their entropy lies in defining the complete solution of such systems, which depends on introducing a method of decomposing their dynamic states from their static states. The solution is formulated by converting the singular system of regular pencils into a recursive form using the sequence of transformations, which separates the dynamic variables from the algebraic variables. The main idea of this work is demonstrated via numerical examples.
ISSN:1099-4300
1099-4300
DOI:10.3390/e20060400