On Laplace transforms with respect to functions and their applications to fractional differential equations

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