Post #525767

This Sunday's #paperOfTheDay is "Solutions to Nonlinear Fractional Duffing Oscillator using MsDTM" from 2026. One possibility to derive #tropicalFieldTheory is a scaling limit of long range interacting field theory, see https://paulbalduf.com/research/tropical-field-theory/tropical-motivation/ . The equation of motion for such theories includes, in place of an ordinary Laplacian (i.e. second derivative), a non-integer derivative operator. There are numerous different ways to define such operators, and they have been studied in various areas of #mathematics and #physics in recent years. Roughly speaking, having a non-integer derivative in a differential equation is equivalent to an integral operator, so that the solutions show much stronger memory and non-locality effects than usual differential equations. The present paper is concerned with a novel method to solve non-integer differential equations numerically. I really like the authors' exposition of the background and broader context. They then display several numerical solution curves they computed, which are nice illustrations of the qualitative effects of the non-integer differential equation under consideration. This paper is a follow-up on another paper that actually introduced the method. The authors make numerous comments how the new method is superior to existing ones, and I agree with this intuitively, but unfortunately they miss the opportunity to show concrete plots or numbers for comparison. Nonetheless interesting work, you learn something new every day (in particular when you do a #dailyPaperChallenge ) https://link.springer.com/article/10.1007/s10773-025-06210-3