In this study, we use a new approach, known as the Aboodh residual power series method (ARPSM), in order to obtain analytical results of Black–Scholes differential equations (BSDEs), which are prime for judgment European call and put options on non-dividend-paying stock, especially when they consist time-fractional derivatives. The fractional derivative is considered Caputo sense. This approach...

let $alpha$ be an automorphism of a ring $r$. the authors [on skewinverse laurent-serieswise armendariz rings, comm. algebra 40(1)(2012) 138-156] applied the concept of armendariz rings to inverseskew laurent series rings and introduced skew inverselaurent-serieswise armendariz rings. in this article, we study on aspecial type of these rings and introduce strongly armendariz ringsof inverse ske...

In this paper, we discuss the usual stochastic‎, ‎likelihood ratio, ‎dispersive and convex transform order between two parallel systems with independent heterogeneous extended generalized exponential components. ‎We also establish the usual stochastic order between series systems from two independent heterogeneous extended generalized exponential samples. ‎Finally, ‎we f...

In this paper, I develop an industry-level index of capital-embodied R&D by capturing the extent of research and development directed at the capital goods in which a given industry invests. Compiling and adjusting data from the National Science Foundation and Commerce Department, I construct industry-level, time-series measures of this index and investigate its properties. The data allow me to ...