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.
Zakaria, M., Moujahid, A. & Ikhouba, M. (2023). A new fractional derivative operator and applications. International Journal of Nonlinear Analysis and Applications, 14(1), 1277–1282. https://doi.org/10.22075/ijnaa.2022.26841.3423
MLA
Zakaria, M., Moujahid, A., & Ikhouba, M. "A new fractional derivative operator and applications", International Journal of Nonlinear Analysis and Applications, 14, 1, 2023, 1277–1282. doi: 10.22075/ijnaa.2022.26841.3423
HARVARD
Zakaria, M., Moujahid, A., & Ikhouba, M. (2023). 'A new fractional derivative operator and applications', International Journal of Nonlinear Analysis and Applications, 14(1), pp. 1277–1282. doi: 10.22075/ijnaa.2022.26841.3423
CHICAGO
Zakaria, M., Moujahid, A. & Ikhouba, M., "A new fractional derivative operator and applications." International Journal of Nonlinear Analysis and Applications, 14 1 (2023): 1277–1282, doi: 10.22075/ijnaa.2022.26841.3423
VANCOUVER
Zakaria M., Moujahid A., Ikhouba M. A new fractional derivative operator and applications. IJNAA. 2023;14(1):1277–1282. doi: 10.22075/ijnaa.2022.26841.3423
International Journal of Nonlinear Analysis and Applications