Dynamical structure of truncated M−fractional Klein–Gordon model via two integral schemes

•Truncated M−fractional Klein–Gordon model via two integral schemes.•Various pattern of solitonic structural solutions which significantly interesting phenomena in nonlinear sciences are constructed successfully.•The mixed solutions in-terms of hyperbolic and sinusoidal functions (periodic rogues, breather waves, breather line wave, bell-shaped line solitons are derived.•Propagation features of the developed solutions can be controlled with the controlling parameter is argued and demonstrated in figures.