On the generalized Fourier transform Articles uri icon

publication date

  • November 2023

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