From Wavelet Analysis to Fractional Calculus: A Review

Emanuel Guariglia (), Rodrigo C. Guido and Gabriel J. P. Dalalana
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Emanuel Guariglia: School of Mathematical Sciences, College of Science and Technology, Wenzhou-Kean University, 88 Daxue Rd, Wenzhou 325060, China
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

Mathematics, 2023, vol. 11, issue 7, 1-12

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.

Keywords: wavelet transform; wavelet basis; multiresolution analysis; fractional derivative; fractional model; fractional system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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