  An important class of fractional differential and integral operators is given
by the theory of fractional calculus with respect to functions, sometimes
called $\Psi$-fractional calculus. The operational calculus approach has proved
useful for understanding and extending this topic of study. Motivated by
fractional differential equations, we present an operational calculus approach
for Laplace transforms with respect to functions and their relationship with
fractional operators with respect to functions. This approach makes the
generalised Laplace transforms much easier to analyse and to apply in practice.
We prove several important properties of these generalised Laplace transforms,
including an inversion formula, and apply it to solve some fractional
differential equations, using the operational calculus approach for efficient
solving.
