On the generalized Fourier transform

On the generalized Fourier transform

In this paper, we introduce the theory of a generalized Fourier transform in order to solve differential equations with a generalized fractional derivative, and we state its main properties. In particular, we obtain the new corresponding convolution, inverse and Plancherel formulas, and Hausdorff–Yo...

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Veröffentlicht in:Mathematical methods in the applied sciences 2023-11, Vol.46 (16), p.16709-16733
Hauptverfasser: Abreu‐Blaya, Ricardo, Rodríguez, José M., Sigarreta, José M.
Format: Artikel
Sprache:eng
Schlagworte:
Fourier transforms
Fractional calculus
Mathematical analysis
Partial differential equations
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Zusammenfassung:In this paper, we introduce the theory of a generalized Fourier transform in order to solve differential equations with a generalized fractional derivative, and we state its main properties. In particular, we obtain the new corresponding convolution, inverse and Plancherel formulas, and Hausdorff–Young type inequality. We show that this generalized Fourier transform is useful in the study of several fractional differential equations (both ordinary and partial differential equations).
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9471