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Generalized Laplace transform and tempered Ψ-Caputo fractional derivative

    Milan Medveď   Affiliation
    ; Michal Pospíšil   Affiliation

Abstract

In this paper, images of the tempered Ψ-Hilfer fractional integral and the tempered Ψ-Caputo fractional derivative under the generalized Laplace transform are derived. The results are applied to find a solution to an initial value problem for a nonhomogeneous linear fractional differential equation with the tempered Ψ-Caputo fractional derivative of an order α for n− 1 <α<n∈N. An illustrative example is given for 0 <α< 1 comparing solutions to the same initial value problem but with different tempering and Ψ.

Keyword : Laplace transform, fractional derivative, fractional differential equation, representation of solution

How to Cite
Medveď, M., & Pospíšil, M. (2023). Generalized Laplace transform and tempered Ψ-Caputo fractional derivative. Mathematical Modelling and Analysis, 28(1), 146–162. https://doi.org/10.3846/mma.2023.16370
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Jan 19, 2023
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