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Abstract New exact solutions of the space–time conformable Caudrey–Dodd–Gibbon (CDG) equation have been derived by implementing the conformable derivative. The generalized Riccati equation mapping method is applied to figure out twenty-seven forms of exact solutions, which are soliton, rational, and periodic ones. Also, for some suitable values of parameters, the exact solutions are found, namely dark, bell type, periodic, soliton, singular soliton, and several others, by using the conformable derivative. These types of solutions have not been proclaimed so far. 2D and 3D graphical patterns of some solutions are also given for clarification of physical features. The conformable derivative is one of the excellent choices to solve the nonlinear conformable problems arising in theory of solitons and many other areas. The results are new and very interesting for the large community of researchers working in the field of mathematics and mathematical physics.