New generalized Fourier transforms and their applications to ordinary, partial and fractional differential equations
Yazarlar (2)
Dr. Öğr. Üyesi Enes Ata Kırşehir Ahi Evran Üniversitesi, Türkiye
Prof. Dr. İsmail Onur KIYMAZ Kırşehir Ahi Evran Üniversitesi, Türkiye
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Miskolc Mathematical Notes | ||
| Dergi ISSN | 1787-2405 Wos Dergi Scopus Dergi | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | İngilizce | Basım Tarihi | 01-2025 |
| Cilt / Sayı / Sayfa | 26 / 2 / 559–577 | DOI | 10.18514/MMN.2025.4509 |
| Makale Linki | https://doi.org/10.18514/mmn.2025.4509 | ||
| UAK Araştırma Alanları |
Uygulamalı Matematik
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| Özet |
| This article presents new generalized definitions of Fourier, Fourier sine, Fourier cosine, inverse Fourier, inverse Fourier sine and inverse Fourier cosine transforms, which encompass various studies on the generalized Fourier transforms in the existing literature. We also give some fundamental properties such that linearity, shifting, differentiability and convolution. Moreover, the solutions to the ordinary electric current differential equation and the fractional motion differential equation are obtained through the use of the generalized Fourier and inverse Fourier transforms. Subsequently, the solutions to the partial diffusion differential equation are obtained through the use of the generalized Fourier sine, inverse Fourier sine, Fourier cosine, and inverse Fourier cosine transforms. Furthermore, we illustrate the relations of the new generalized Fourier transforms with other the generalized Fourier transforms available in the literature. Finally, we provide tables of the new generalized Fourier transforms, and then graphs of the approximate behaviours of the solution of the ordinary electric current differential equation. |
| Anahtar Kelimeler |
| Fourier transform | fractional derivatives and integrals | fractional differential equations | ordinary differential equations | partial differential equations |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| Scopus | 1 |