%0 Journal Article
%T A new fractional derivative operator and applications
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Zakaria, Mouhssine
%A Moujahid, Abdelaziz
%A Ikhouba, Mahjoub
%D 2023
%\ 01/01/2023
%V 14
%N 1
%P 1277-1282
%! A new fractional derivative operator and applications
%K New Fractional Derivative
%K Fractional differential equations
%K Caputo differential operators
%R 10.22075/ijnaa.2022.26841.3423
%X 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.
%U https://ijnaa.semnan.ac.ir/article_7003_5c8f6ff4033fccd6eadc0fd001ee4ac8.pdf