From Wavelet Analysis to Fractional Calculus: A Review
Abstract
:1. Introduction
2. Historical Note on Wavelet Analysis
2.1. From Fourier Analysis to Haar Function Analysis
2.2. New Perspectives: The Beginning of the Wavelet Dawn
2.3. From Grossmann and Morlet to Modern Approaches
3. Wavelet Analysis—An Application Overview
3.1. Signal Processing and Image Compression
3.2. Electromagnetism
3.3. PDEs and Integral Equations
3.4. Astronomy
3.5. Acoustics
3.6. Biomedicine
4. Historical Note on Fractional Calculus
5. Fractional Calculus—An Application Overview
5.1. Control Theory
5.2. Electromagnetism
5.3. Quantum Mechanics
5.4. Signal Theory
5.5. Cryptography
5.6. Image Processing
5.7. Biology
5.8. Epidemiology and COVID-19
6. Conclusions
Funding
Acknowledgments
Conflicts of Interest
References
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Guariglia, E.; Guido, R.C.; Dalalana, G.J.P. From Wavelet Analysis to Fractional Calculus: A Review. Mathematics 2023, 11, 1606. https://doi.org/10.3390/math11071606
Guariglia E, Guido RC, Dalalana GJP. From Wavelet Analysis to Fractional Calculus: A Review. Mathematics. 2023; 11(7):1606. https://doi.org/10.3390/math11071606
Chicago/Turabian StyleGuariglia, Emanuel, Rodrigo C. Guido, and Gabriel J. P. Dalalana. 2023. "From Wavelet Analysis to Fractional Calculus: A Review" Mathematics 11, no. 7: 1606. https://doi.org/10.3390/math11071606
APA StyleGuariglia, E., Guido, R. C., & Dalalana, G. J. P. (2023). From Wavelet Analysis to Fractional Calculus: A Review. Mathematics, 11(7), 1606. https://doi.org/10.3390/math11071606