New explicit solitons for the general modified fractional Degasperis-Procesi-Camassa-Holm equation with a truncated M-fractional derivative

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.