On the soliton structures to the space-time fractional generalized reaction Duffing model and its applications - Tariq, Kalim U.; İnç, Mustafa; Hashemi, Mir Sajjad (Springer, 2024)
In this study, the space-time fractional generalised reaction duffing model is investigated analytically, which is a generalization for a collection of prominent fractional models describing various key phenomenon in science and engineering. The governing equation is converted to a nonlinear ODE by the compatible travelling wave transform. The investigation established that for analysing nonlinear evolution equations of fractional order, the recommended approach is more effective and realistic. The findings are given extensively in rational forms of trigonometric function series or clearly in powers of specific trigonometric functions. A collection of bright, dark, periodic, and optical solitons is discovered. Mathematica is used to flourish the presence of some obtained solutions in 3D graphs with different fractional orders. The results show that the recommended methods are more practical and effective ways to illustrate the dynamics of several complex wave structures in modern science and technology.
Keywords: Solitary wave solution; Fractional model; Solitons; Analytical solutions; Nonlinear evolution equations; Traveling wave solutions.