| Yazarlar (2) |
Enes Ata
Kırşehir Ahi Evran Üniversitesi, Turkey |
Prof. Dr. İsmail Onur KIYMAZ
Kırşehir Ahi Evran Üniversitesi, Türkiye |
| Özet |
| In this paper, we reconstruct gamma and beta functions using a general kernel function in their integral representations. We also reconstruct the Gauss and confluent hypergeometric functions using the beta function with general kernel in their series representations. The general kernel function we use here can be chosen as any special function such as the exponential function, Mittag-Leffler function, Wright function, Fox-Wright function, Kummer function or M-series. Using different choices of this general kernel function, various of the generalized gamma, beta, Gauss hypergeometric and confluent hypergeometric functions in literature can be obtained. In this paper, we first obtain the integral representations, functional relations, summation, derivative and transformation formulas and double Laplace transforms of the special functions we construct. Furthermore, we compute the solutions of some fractional partial differential equations involving special functions with general kernel via the double Laplace transform and graph some of the solutions for specific values. Finally, we obtain the incomplete beta function with general kernel by defining the beta distribution with general kernel. |
| Anahtar Kelimeler |
| Fractional derivatives and integrals | Fractional partial differential equations | Gamma and Beta functions | Gauss and Confluent hypergeometric functions | Laplace transform |
| Makale Türü | Özgün Makale |
| Makale Alt Türü | SCOPUS dergilerinde yayımlanan tam makale |
| Dergi Adı | International Journal of Mathematics and Computer in Engineering |
| Dergi ISSN | 2956-7068 |
| Makale Dili | İngilizce |
| Basım Tarihi | 12-2025 |
| Cilt No | 3 |
| Sayı | 2 |
| Sayfalar | 153 / 170 |
| Doi Numarası | 10.2478/ijmce-2025-0013 |
| Atıf Sayıları | |
| SCOPUS | 1 |
| Google Scholar | 4 |
