On nth Level Fractional Derivatives: An Equivalent Representation and Applications to Inverse Problem

Abstract: This work contributes to the theory of nth level fractional derivative, where $n$ is a positive integer. An equivalent representation of 2nd level fractional derivative in terms of Riemann-Liouville fractional derivative is presented. We generalized our result and provide representation of nth level fractional derivative. As an application, we solve an inverse problem defined for a diffusion equation involving 2nd level fractional derivative.