On the generalized Fourier transform
Journal
Mathematical Methods in the Applied Sciences
ISSN
1099-1476
Date Issued
2023-06-21
Author(s)
Abstract
<jats:p>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).</jats:p>