MMN-4509
New generalized Fourier transforms and their applications to ordinary, partial and fractional differential equations
Enes Ata; İ. Onur Kıymaz;Abstract
In this article, the new generalized Fourier, Fourier sine, Fourier cosine, inverse Fourier, inverse Fourier sine and inverse Fourier cosine transformations, which are more general and cover the studies in the literature, are defined and their properties are given. Furthermore, the solutions of the ordinary electric current and fractional motion differential equations are obtained with the help of generalized Fourier transform, and then the solution of the partial diffusion differential equation is obtained with the help of generalized Fourier sine and Fourier cosine transforms. Finally, the tables of the new generalized Fourier transforms, the graps of approximate solutions of the ordinary electric current differential equation, and the relations of the new generalized Fourier transforms with other Fourier transforms which can be found in the literature are presented.
Vol. 26 (2025), No. 2, pp. 559-577