Fig. 1
2D, time evolution (at t = 0, 1, 2) and 3D plots show the two-peak M-type soliton solution W2,2 using m = 0.3, l = 0.6, n = 0.2, A = − 4, B = 1, C = 0, P = 1, Q = 3, σ =− 0.2, µ = 0.4 and different fractional derivatives (a) Illustrates the solution using fractional order 0.6 and β -Derivative, (b) Shows the solution using fractional order 0.6,\(\gamma\) = 1.3 and M-Truncated Derivative. (c) Shows Conformable Derivative using fractional order 0.6. The solitons show a central peak with slight changes in width and amplitude, confirming the symmetry of the travelling wave, showing that the soliton preserves its overall shape using different derivative types.
