Journal
FRACTAL AND FRACTIONAL
Volume 7, Issue 7, Pages -Publisher
MDPI
DOI: 10.3390/fractalfract7070524
Keywords
operational calculus; Mellin transform; fractional scale-invariant; fractional scale derivative; stretching derivative; hadamard derivative
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The paper introduces and studies fractional scale-invariant systems using an operational formalism. It is shown that the impulse and step responses of these systems belong to the vector space generated by special functions introduced in the paper. The method's effectiveness and accuracy are demonstrated through various numerical simulations.
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.
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