Important analytical methods such as the methods of exp-function, rational hyperbolic method (RHM) and sec–sech method are applied in this paper to solve fractional nonlinear partial differential equations (FNLPDEs) with a truncated M-fractional derivative (TMFD), which consist of exponential terms. A general modified fractional Degasperis–Procesi–Camassa–Holm equation (GM-FDP-CHE) is investigated with TMFD. The exp-function method is also applied to derive a variety of traveling wave solutions (TWSs) with distinct physical structures for this nonlinear evolution equation. The RHM is used to obtain single-soliton solutions for this equation. The sec–sech method is used to derive multiple-soliton solutions of the GM-FDP-CHE. These techniques can be implemented to find various differential equations exact solutions arising from problems in engineering. The analytical solution of the M-fractional heat equation is found. Graphical representations are also given.

中文翻译：

---

具有截断 M-分数导数的一般改进分数 Degasperis-Procesi-Camassa-Holm 方程的新显式孤子

本文采用重要的分析方法，如 exp 函数、有理双曲线法 (RHM) 和 sec-sech 法来求解截断的分数非线性偏微分方程 (FNLPDE)米-分数导数 (TMFD)，由指数项组成。使用 TMFD 研究了一般改进的分数 Degasperis-Procesi-Camassa-Holm 方程 (GM-FDP-CHE)。exp 函数方法也被用于推导该非线性演化方程具有不同物理结构的各种行波解 (TWS)。RHM 用于获得该方程的单孤子解。sec-sech 方法用于导出 GM-FDP-CHE 的多孤子解。可以实施这些技术来找到由工程问题引起的各种微分方程的精确解。的解析解米-找到分数热方程。还给出了图形表示。