More properties of the proportional fractional integrals and derivatives of a function with respect to another function

More properties of the proportional fractional integrals and derivatives of a function with respect to another function

In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the derivatives in the Riemann–Liouville setting and the one in Caputo. In addition, we provid...

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Veröffentlicht in:Advances in difference equations 2020-06, Vol.2020 (1), p.1-16, Article 303
Hauptverfasser: Jarad, Fahd, Abdeljawad, Thabet, Rashid, Saima, Hammouch, Zakia
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Derivatives
Difference and Functional Equations
Functional Analysis
General Caputo proportional derivative
General proportional derivatives
General proportional integrals
Laplace transforms
Mathematics
Mathematics and Statistics
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
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Beschreibung
Zusammenfassung:In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the derivatives in the Riemann–Liouville setting and the one in Caputo. In addition, we provide an integration by parts formulas related to the considered operators.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-02767-x