New generalized special functions with two generalized M-series at their kernels and solution of fractional PDEs via double Laplace transform
Yazarlar (2)
Kırşehir Ahi Evran Üniversitesi, Türkiye
Prof. Dr. İsmail Onur KIYMAZ
Kırşehir Ahi Evran Üniversitesi, Türkiye
| Makale Türü | Özgün Makale (ESCI dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Computational Methods for Differential Equations | ||
| Dergi ISSN | 2345-3982 Wos Dergi Scopus Dergi | ||
| Dergi Tarandığı Indeksler | ESCI | ||
| Makale Dili | Türkçe | Basım Tarihi | 01-2024 |
| Cilt / Sayı / Sayfa | 12 / 1 / 31–43 | DOI | 10.22034/cmde.2023.55800.2325 |
| Makale Linki | chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://cmde.tabrizu.ac.ir/article_16751_7023d19494e120b6533563352438c893.pdf | ||
| Özet |
| In this paper, we introduce three types of generalized special functions: beta, Gauss hypergeometric, and confluent hypergeometric, all involving two generalized M-series at their kernels. We then give several properties of these functions, such as integral representations, functional relations, summation relations, derivative formulas, transformation formulas, and double Laplace transforms. Furthermore, we obtain solutions of fractional partial differential equations involving these new generalized special functions and then we present graphs of the approximate behavior of the solutions. Also, we introduce a new generalized beta distribution and incomplete beta function. Finally, we establish relationships between the new generalized special functions and other generalized special functions found in the literature. |
| Anahtar Kelimeler |
| Beta function | Confluent hypergeometric function | Double Laplace transform | Fractional partial differential equations | Gauss hypergeometric function |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| SCOPUS | 4 |
| Google Scholar | 7 |