HYPERBOLIC FRACTIONAL DIFFERENTIAL OPERATOR

Abstract

In this paper, we introduce a new definition of fractional derivative by using the limit approach and based on hyperbolic functions for α ∈ (0, 1] which obeys classical properties including linearity, product rule and many fractional versions of other properties and results, such as Rolle’s theorem, and the mean value theorem. Further, if α = 1, the definition coincides with the classical definition of first derivative. We give some applications to fractional differential equations.