A new fractional derivative operator with a generalized exponential kernel.

This paper is mainly concerned with introducing a new fractional derivative operator with a generalized exponential kernel. The benefit of the new definition over existing exponential kernel operators is that it is possible to extend the new operator to a fractional derivative operator with a singular kernel. We introduced the corresponding fractional integral operator and the extended derivative operator which includes integrable singular kernel. Furthermore, we expressed the new fractional derivative and integral operators as convergent series in terms of the Riemann–Liouville integral operator. Some relationships, characteristics and comparisons with other operators were studied. Finally, we discussed the dynamics of a nonlinear fractional order model incorporating the proposed extended fractional derivative. [ABSTRACT FROM AUTHOR]