Differential equations with tempered Ψ-Caputo fractional derivative

• Published in: Mathematical modelling and analysis Vol. 26; no. 4; pp. 631 - 650
• Main Authors: Medveď, Milan, Brestovanská, Eva
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 26.11.2021
• Subjects: Cauchy problems; Differential equations; Existence theorems; Fractional calculus; Inequality; Linear systems; Mathematical analysis; tempered riemann-liouville fractional derivative; tempered ψ−caputo fractional derivative; tempered Riemann-Liouville fractional derivative; tempered Ψ−Caputo fractional derivative

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 ty...