We study a fifth order time-fractional KdV equation (FKdV) under meaning of the conformal fractional derivative. By trial equation method based on symmetry, we construct the abundant exact traveling wave solutions to the FKdV equation. These solutions show rich evolution patterns including solitons, rational singular solutions, periodic and double periodic solutions and so forth. In particular, under the concrete parameters, we give the representations of all these solutions.

Chinese shale reservoirs are typically deep, clay-rich, and highly water-sensitive, which severely limits the effectiveness of conventional hydraulic fracturing. To address this challenge, we propose a microwave-assisted waterless fracturing method and investigate its feasibility through laboratory experiments on core samples from the Gulong shale and tight sandstone formations in the Daqing Oilfield. A coupled model integrating microwave power dissipation, pore water heating, and thermal stress evolution is developed to interpret the underlying mechanisms. Experimental results show that, under microwave irradiation (200 W, 40 s) and initial pore water content of 2.1–6%, fracturing is successfully induced without external fluid injection. The tensile failure of the rock coincides with the peak internal pore pressure generated by rapid vaporization and thermal expansion of pore water, as confirmed by a modified tensile strength measurement method. Fracture patterns observed in SEM and post-treatment imaging align with model predictions, demonstrating that microwave energy absorption by pore water is the primary driver of rock failure. The technique eliminates water-related formation damage and is inherently suitable for deep, water-sensitive reservoirs. This study provides experimental evidence and mechanistic insight supporting microwave-based waterless fracturing as a viable approach for challenging shale formations.