The causal
            <i>α</i>
            -exponential and the solution of fractional linear time-invariant systems

Bengochea, G.; Ortigueira, M.; Verde-Star, L.

doi:10.1080/00207721.2024.2321369

International Journal of Systems Science

2024

DOI: 10.1080/00207721.2024.2321369

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The causal α -exponential and the solution of fractional linear time-invariant systems

G. Bengochea,

M. Ortigueira,

L. Verde-Star

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2024

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Cited by 2 publications

References 34 publications

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Searching for Sonin kernels

Ortigueira

2024

Fract Calc Appl Anal

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The causal shift-invariant convolution is studied from the point of view of inversion. Abel’s algorithm, used in the tautochrone problem, is considered and Sonin’s existence condition is deduced. To generate pairs of functions verifying Sonin’s condition, the class of Mittag-Leffler type functions is used. In particular, functions that are impulse responses of ARMA(N,N) systems serve as a basis. The possible use of Abel’s procedure as a support for introducing generalized fractional derivatives is evaluated.

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Searching for Sonin kernels

Ortigueira

2024

Fract Calc Appl Anal

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Variable-Order Fractional Scale Calculus

Valério,

Ortigueira

2023

Mathematics

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General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and discussed. Fractional variable-order systems of autoregressive–moving-average type are introduced and exemplified. The corresponding transfer functions are obtained and used to find the corresponding impulse responses.

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The causal α -exponential and the solution of fractional linear time-invariant systems

Cited by 2 publications

References 34 publications

Searching for Sonin kernels

Searching for Sonin kernels

Variable-Order Fractional Scale Calculus

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