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An Operational Approach to Fractional Scale-Invariant Linear Systems
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Resumo(s)
The fractional scale-invariant systems are introduced and studied, using an operational formalism. It is shown that the impulse and step responses of such systems belong to the vector space generated by some special functions here introduced. For these functions, the fractional scale derivative is a decremental index operator, allowing the construction of an algebraic framework that enables to compute the impulse and step responses of such systems. The effectiveness and accuracy of the method are demonstrated through various numerical simulations.
Descrição
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© 2023 by the authors.
Palavras-chave
fractional scale derivative fractional scale-invariant hadamard derivative Mellin transform operational calculus stretching derivative Analysis Statistical and Nonlinear Physics Statistics and Probability