Fractional derivative of power type functions

Bengochea Gabriel; Ortigueira Manuel

doi:10.1007/s40314-022-02081-0

Fractional derivative of power type functions

Bengochea Gabriel, Ortigueira Manuel

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Abstract

Non-square integrable, power type, signals are introduced and studied with generality. The problems associated with the definition of their suitable fractional derivatives are discussed and solved. Two particular, very important, cases are treated with detail: the almost periodic signals and the stationary stochastic processes. For them, correlations and corresponding generalized harmonic analysis are introduced and studied.

Original language	English
Number of pages	18
Journal	Computational and Applied Mathematics
Volume	41
Issue number	8
DOIs	https://doi.org/10.1007/s40314-022-02081-0
Publication status	Published - Dec 2022

Keywords

Power type signal
Almost periodic
Unified fractional derivative
Autocorrelation

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10.1007/s40314-022-02081-0

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title = "Fractional derivative of power type functions",

abstract = "Non-square integrable, power type, signals are introduced and studied with generality. The problems associated with the definition of their suitable fractional derivatives are discussed and solved. Two particular, very important, cases are treated with detail: the almost periodic signals and the stationary stochastic processes. For them, correlations and corresponding generalized harmonic analysis are introduced and studied.",

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author = "Bengochea Gabriel and Ortigueira Manuel",

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AU - Manuel, Ortigueira

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N2 - Non-square integrable, power type, signals are introduced and studied with generality. The problems associated with the definition of their suitable fractional derivatives are discussed and solved. Two particular, very important, cases are treated with detail: the almost periodic signals and the stationary stochastic processes. For them, correlations and corresponding generalized harmonic analysis are introduced and studied.

AB - Non-square integrable, power type, signals are introduced and studied with generality. The problems associated with the definition of their suitable fractional derivatives are discussed and solved. Two particular, very important, cases are treated with detail: the almost periodic signals and the stationary stochastic processes. For them, correlations and corresponding generalized harmonic analysis are introduced and studied.

KW - Power type signal

KW - Almost periodic

KW - Unified fractional derivative

KW - Autocorrelation

U2 - 10.1007/s40314-022-02081-0

DO - 10.1007/s40314-022-02081-0

M3 - Article

SN - 2238-3603

VL - 41

JO - Computational and Applied Mathematics

JF - Computational and Applied Mathematics

IS - 8

ER -

Fractional derivative of power type functions

Abstract

Keywords

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