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From Wavelet Analysis to Fractional Calculus: A Review

Author

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  • Emanuel Guariglia

    (School of Mathematical Sciences, College of Science and Technology, Wenzhou-Kean University, 88 Daxue Rd, Wenzhou 325060, China
    Institute of Biosciences, Letters and Exact Sciences, Rua Cristóvão Colombo 2265, São Paulo State University (UNESP), São José do Rio Preto 15054-000, SP, Brazil)

  • Rodrigo C. Guido

    (Institute of Biosciences, Letters and Exact Sciences, Rua Cristóvão Colombo 2265, São Paulo State University (UNESP), São José do Rio Preto 15054-000, SP, Brazil)

  • Gabriel J. P. Dalalana

    (Institute of Biosciences, Letters and Exact Sciences, Rua Cristóvão Colombo 2265, São Paulo State University (UNESP), São José do Rio Preto 15054-000, SP, Brazil)

Abstract

In this note, we review some important results on wavelets, together with their main applications. Similarly, we present the main results on fractional calculus and their current applications in pure and applied science. We conclude the paper showing the close interconnection between wavelet analysis and fractional calculus.

Suggested Citation

  • Emanuel Guariglia & Rodrigo C. Guido & Gabriel J. P. Dalalana, 2023. "From Wavelet Analysis to Fractional Calculus: A Review," Mathematics, MDPI, vol. 11(7), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1606-:d:1107900
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    References listed on IDEAS

    as
    1. Gilardi-Velázquez, H.E. & Echenausía-Monroy, J.L. & Jaimes-Reátegui, R. & García-López, J.H. & Campos, Eric & Huerta-Cuellar, G., 2022. "Deterministic coherence resonance analysis of coupled chaotic oscillators: fractional approach," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Baba, Isa Abdullahi & Rihan, Fathalla A., 2022. "A fractional–order model with different strains of COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
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