Document Type : Research Paper

Authors

• Mouhssine Zakaria
• Abdelaziz Moujahid
• Mahjoub Ikhouba

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

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:
$$D^{\alpha }(f)(t)=\underset{ϵ\to 0}{lim}\frac{f\left(t{e}^{\frac{1}{\mathrm{\Gamma }(1-\alpha )}}{e}^{-\alpha }\right)-f(t)}{ϵ},$$
this definition is comfortable with the classical definition of the Caputo Fractional Operator.

Keywords

• New Fractional Derivative
• fractional differential equations
• Caputo differential operators