Over the past three decades, fractional calculus has gained increasing importance and practical relevance in various fields of science and engineering. This article aims to develop enhanced ...

Various classes of analytic, quasi-analytic and other infinitely differentiable functions of a real variable are studied. The paper gives a self-contained treatment by means of an elementary real ...

Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...

A novel differentiable approach optimizes geometric waveguide coatings, achieving substantial gains in light efficiency and ...

The original version of this story appeared in Quanta Magazine. Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky ...