AUTHOR=Niu Jing-Yan , Feng Guang-Qing , Gepreel Khaled A. TITLE=A simple frequency formulation for fractal–fractional non-linear oscillators: A promising tool and its future challenge JOURNAL=Frontiers in Physics VOLUME=11 YEAR=2023 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1158121 DOI=10.3389/fphy.2023.1158121 ISSN=2296-424X ABSTRACT=

This paper proposes a simple frequency formula developed from He’s frequency formulation for fractal systems. In this approach, the initial guess can be judiciously chosen. Even the simplest initial guess leads to a highly accurate approximate solution. A detailed theoretical development is elucidated, and the solving process is given step by step. The simple calculation and reliable results have been merged into an effective tool for deeply studying fractal vibration systems, and the present approach offers a completely new angle for the fast insight into the physical properties of a non-linear vibration system in a fractal space.