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Introducing novel $(\psi,\phi)$-fractional operators advances in fractional calculus | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 اردیبهشت 1404 اصل مقاله (1.23 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.62416.2748 | ||
| نویسنده | ||
| Lakhlifa Sadek* | ||
| Department of Mathematics, Faculty of Sciences and Technology, BP 34. Ajdir 32003 Al-Hoceima, Abdelmalek Essaadi University, Tetouan, Morocco. | ||
| چکیده | ||
| This study introduces novel generalized fractional derivatives known as $(\psi,\phi)$-fractional derivatives of the Riemann-Liouville and Caputo types, each incorporating exponential function kernels. These new operators offer distinct advantages, including a semi-group property and a seamless extension of the Riemann-Liouville (RL-FD) and Caputo fractional derivatives (C-FD), as well as integrals (RL-FI). We explore the Laplace transform of these $(\psi,\phi)$-fractional derivatives and $(\psi,\phi)$-integral, leveraging them to address linear $(\psi,\phi)$-fractional differential equations. Moreover, these fractional operators are general to classical fractional operators, cotangent fractional operators, and generalized proportional operators. | ||
| کلیدواژه‌ها | ||
| $(\psi؛ \phi)$-fractional operators؛ Laplace transform؛ linear $(\psi؛ \phi)$-fractional differential equations | ||
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آمار تعداد مشاهده مقاله: 54 تعداد دریافت فایل اصل مقاله: 61 |
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