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CMMSE: On the generalized Fourier transform
  • Ricardo Abreu Blaya,
  • José M. Rodríguez,
  • José M. Sigarreta
Ricardo Abreu Blaya
Universidad Autónoma de Guerrero

Corresponding Author:[email protected]

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José M. Rodríguez
Universidad Carlos III de Madrid
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José M. Sigarreta
Universidad Autonoma de Guerrero - Campus Acapulco
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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 corresponding convolution, inverse and Plancherel formulas, and Hausdorff-Young inequality. We show that this generalized Fourier transform is useful in the study of fractional partial differential equations, by solving the fractional heat equation on the real line.
27 Jul 2022Submitted to Mathematical Methods in the Applied Sciences
28 Jul 2022Submission Checks Completed
28 Jul 2022Assigned to Editor
14 Aug 2022Reviewer(s) Assigned
03 Mar 2023Review(s) Completed, Editorial Evaluation Pending
13 Mar 2023Editorial Decision: Revise Major
22 Mar 20231st Revision Received
22 Mar 2023Submission Checks Completed
22 Mar 2023Assigned to Editor
22 Mar 2023Review(s) Completed, Editorial Evaluation Pending
28 Mar 2023Reviewer(s) Assigned
24 May 2023Editorial Decision: Accept