TY - JOUR
ID - 7003
TI - A new fractional derivative operator and applications
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Zakaria, Mouhssine
AU - Moujahid, Abdelaziz
AU - Ikhouba, Mahjoub
AD - Department of Mathematics, Faculty of Science Tetouan, Abdelmalek Essaad University, Tetouan, Morocco
Y1 - 2023
PY - 2023
VL - 14
IS - 1
SP - 1277
EP - 1282
KW - New Fractional Derivative
KW - Fractional differential equations
KW - Caputo differential operators
DO - 10.22075/ijnaa.2022.26841.3423
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_7003.html
L1 - https://ijnaa.semnan.ac.ir/article_7003_5c8f6ff4033fccd6eadc0fd001ee4ac8.pdf
ER -