A Generalised Continuous Primitive Integral and Some of its Applications

Using the Laplace derivative a Perron type integral, is defined. Moreover, it shown that this integral includes and to show inclusion proper, an example of function constructed, which integrable but not integrable. Properties integrals such as fundamental theorem calculus, Hake's theorem, integration by parts, convergence theorems, mean value remainder form Taylor's with estimation remainder, are established. It turns out concerning Alexiewicz norm, space all functions incomplete contains set polynomials densely. Applications Poisson system generalised ordinary differential equations higher-order equation.