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

Jarad, FahdJarad, FahdAbdeljawad, ThabetAbdeljawad, ThabetRashid, SaimaHammouch, Zakia2022-06-202022-06-202020Jarad, Fahd...et al. (2020). "More properties of the proportional fractional integrals and derivatives of a function with respect to another function", Advances in Difference Equations, Vol. 2020, No. 1.1687-1839https://hdl.handle.net/20.500.12416/5681In 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. © 2020, The Author(s).eninfo:eu-repo/semantics/openAccessGeneral Caputo Proportional DerivativeGeneral Proportional DerivativesGeneral Proportional IntegralsMore properties of the proportional fractional integrals and derivatives of a function with respect to another functionMore Properties of the Proportional Fractional Integrals and Derivatives of a Function With Respect To Another FunctionArticle2020110.1186/s13662-020-02767-x