On the generalized Fourier transform Articles uri icon

publication date

  • November 2023

start page

  • 16709

end page

  • 16733

issue

  • 16

volume

  • 46

International Standard Serial Number (ISSN)

  • 0170-4214

Electronic International Standard Serial Number (EISSN)

  • 1099-1476

abstract

  • 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).

keywords

  • fractional derivative; generalized fourier transform