Green's function for the three-variable Laplace equation

Mathematics

Evolutionary biology

Biology

Partial differential equation

Laplace transform

Fractional calculus

Mathematical analysis

Function (biology)

Inverse Laplace transform

Differential equation

Applied mathematics

Mittag-Leffler function

Ordinary differential equation

Advances in Difference Equations

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.

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