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Ultralow-frequency dust acoustic waves in plasma are an important branch of study in plasma physics. Due to the important application of dust acoustic waves in the space environment, industrial processing, and the laboratory, they have aroused great interest in physics and other disciplines. In this paper, dust acoustic waves in dust plasma containing double-temperature ions are studied. According to the equations of dust plasma motion considering the higher order perturbation factors, the (3 + 1)-dimensional Kadomtsev–Petviashvili equation is derived by using multiscale analysis and reduced perturbation methods. The result is a three-dimensional model describing the propagation of waves in space. Compared with the low-dimensional model, this model is more closely aligned with the actual physical situation. Further, to better comprehend the propagation features of dust acoustic waves in plasmas, with the help of the semi-inverse method and the fractional variational principle, the (3 + 1)-dimensional time-space-fractional Kadomtsev–Petviashvili equation is deduced. At the same time, based on the Lie symmetry analysis method, the conservation laws of the time-fractional Kadomtsev–Petviashvili equation are discussed, and the conserved quantities of dust acoustic waves in dual-temperature plasma are obtained. Finally, by virtue of the fractional subequation method, three types of exact analytical solutions of fractional Kadomtsev–Petviashvili equations are given. Drawing on the chirp concept in optical soliton communication, the chirp effect of ultralow-frequency dust acoustic waves is discussed, and the effects of dust temperature, ion temperature, and fractional order on dust acoustic waves in a dual-temperature plasma are studied using the analytical solutions.