Analytic solutions of fractional order physical equations are very significant to explain the behavior of mathematical models expressing complex phenomena in engineering and natural sciences. The modified extended tanh-function (METHF) method is an especially capable and highly effective mathematical technique to attain analytic traveling wave solutions. This research proposes to examine the analytic solutions of the time-fractional $(2+1)$-dimensional non-linear Heisenberg ferromagnetic spin chain (HFSC) equation that describes electromagnetic waves in modern magnet theory by using the suggested method and the definition of conformable fractional derivative. We obtain some new analytic solutions of the proposed equation in terms of hyperbolic, trigonometric, and rational functions. The validity and precision of these solutions are also examined. The 2D, 3D, and contour graphs of solutions are given to manifest the physical behavior of the waves with the aid of the Mathematica package program.

分数阶物理方程的解析解对于解释表达工程和自然科学中复杂现象的数学模型的行为非常重要。改进的扩展 tanh 函数 (METHF) 方法是获得解析行波解的一种特别有能力和高效的数学技术。本研究建议检查时间分数阶的解析解$(2+1)$一维非线性海森堡铁磁自旋链 (HFSC) 方程，它通过使用建议的方法和符合分数阶导数的定义描述现代磁理论中的电磁波。我们根据双曲函数、三角函数和有理函数获得了所提出方程的一些新解析解。还检查了这些解决方案的有效性和精确性。借助 Mathematica 程序包，给出解的 2D、3D 和等高线图以显示波的物理行为。