@article {
author = {Zakaria, Mouhssine and Moujahid, Abdelaziz and Ikhouba, Mahjoub},
title = {A new fractional derivative operator and applications},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {14},
number = {1},
pages = {1277-1282},
year = {2023},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2022.26841.3423},
abstract = {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.},
keywords = {New Fractional Derivative,Fractional differential equations,Caputo differential operators},
url = {https://ijnaa.semnan.ac.ir/article_7003.html},
eprint = {https://ijnaa.semnan.ac.ir/article_7003_5c8f6ff4033fccd6eadc0fd001ee4ac8.pdf}
}