This paper deals with a new numerical method for the approximation of early exercise boundary in American option pricing problem. In more detail, using mean-value theorem integrals, we provide flexible algorithm that allows reaching accurate solution fewer calculations rather than other previously described methods.

A general uniform convergence theorem for numerical integration of Cauchy principal value integrals is proved. Seven special instances of this theorem are given as corollaries.

We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of relations nth-weighted integrals and derivatives. As an application, mean value theorems operators are obtained. Direct corollaries allow one to obtain recent Caputo–Fabrizio, Atangana–Baleanu–Caputo (ABC) ABC

We show that for any two continuous real valued functions f, g on [0, 1], the problemZ 1