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GENERALIZED FOURIER TRANSFORM: ILLUSTRATIVE EXAMPLES AND APPLICATIONS TO DIFFERENTIAL EQUATIONS.
- Source :
-
Journal of Mathematical Analysis . 2024, Vol. 15 Issue 2, p14-33. 20p. - Publication Year :
- 2024
-
Abstract
- In this paper, we define generalized Fourier and inverse Fourier transforms containing the h-exponential function in their kernels and give the fundamental properties of these transforms. We also compute the transforms of both the classical and the generalized Riemann-Liouville and Caputo fractional operators. In addition, we compute the transforms of some elementary and generalized special functions as well. Finally, as applications, we obtain the solutions of two differential equations with ordinary and fractional derivatives using the transforms we have defined. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 21173419
- Volume :
- 15
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 177139658
- Full Text :
- https://doi.org/10.54379/JMA-2024-2-2