A new fractional derivative operator and applications

Document Type : Research Paper


Department of Mathematics, Faculty of Science Tetouan, Abdelmalek Essaad University, Tetouan, Morocco


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.


Volume 14, Issue 1
January 2023
Pages 1277-1282
  • Receive Date: 12 April 2022
  • Accept Date: 16 June 2022