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

By Fahd Jarad, Thabet Abdeljawad, Saima Rashid, Zakia Hammouch. 2020

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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.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/16d2125e71a32babed2cc55f27c654d344ca2275