A new fractional derivative operator and applications | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 98، دوره 14، شماره 1، فروردین 2023، صفحه 1277-1282 اصل مقاله (353.36 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.26841.3423 | ||
| نویسندگان | ||
| Mouhssine Zakaria* ؛ Abdelaziz Moujahid؛ Mahjoub Ikhouba | ||
| Department of Mathematics, Faculty of Science Tetouan, Abdelmalek Essaad University, Tetouan, Morocco | ||
| چکیده | ||
| We introduce a new fractional derivative which obeys classical properties including linearity, product rule, power rule, vanishing derivatives for constant functions, chain rule, quotient rule, Rolle's Theorem and the Mean Value Theorem: $$ D^\alpha(f)(t)=\lim _{\epsilon \rightarrow 0} \frac{f\left(t e^{\frac{1}{\Gamma(1-\alpha)}} e^{-\alpha}\right)-f(t)}{\epsilon}, $$ this definition is comfortable with the classical definition of the Caputo Fractional Operator. | ||
| کلیدواژهها | ||
| New Fractional Derivative؛ fractional differential equations؛ Caputo differential operators | ||
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