Differential equations with tempered Ψ-Caputo fractional derivative

    Milan Medveď Affiliation
    ; Eva Brestovanská Affiliation


In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative. The Cauchy problem for fractional differential equations with this type of derivative is discussed and some existence and uniqueness results are proved. We present a Henry-Gronwall type inequality for an integral inequality with the tempered Ψ−fractional integral. This inequality is applied in the proof of an existence theorem. A result on a representation of solutions of linear systems of Ψ−Caputo fractional differential equations is proved and in the last section an example is presented.

Keyword : tempered Riemann-Liouville fractional derivative, tempered Ψ−Caputo fractional derivative

How to Cite
Medveď, M., & Brestovanská, E. (2021). Differential equations with tempered Ψ-Caputo fractional derivative. Mathematical Modelling and Analysis, 26(4), 631-650.
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Nov 26, 2021
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