Unique solutions, stability and travelling waves for some generalized fractional differential problems

The type of symmetry exhibited by a travelling wave can have important implications for its behaviour and properties, such as polarization, dispersion, interactions with other waves or boundaries. fractional differential Duffing problem refers to the mathematical modelling nonlinear, damped oscillations system derivatives. It is generalization classical equation, which describes oscillator (the equation becomes symmetric under time-reversal). derivatives allow more accurate description system's memory hereditary properties. solution provide insight into complex dynamic various physical, biological, engineering systems. We are concerned studying new problem. involves some sequential Caputo an infinite series Riemann–Liouville integrals functions. begin proving first existence uniqueness result, then we discuss two types stability obtained result. An illustrative examples given show applicability also applying Tanh method obtain classes solutions three (Khalil) conformable problems; generalized Duffing, Landau–Ginzburg–Higgs Sine–Gordon one. Some numerical simulations plotted conclusion at end.