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

Asim Ilyas; Salman A. Malik; Kamran Suhaib

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arXiv · 2506.12614

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

Asim Ilyas·Salman A. Malik·Kamran Suhaib

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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.

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Asim Ilyas, Salman A. Malik, Kamran Suhaib. 2025-06-14. On nth Level Fractional Derivatives: An Equivalent Representation and Applications to Inverse Problem. https://arxiv.org/abs/2506.12614

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