This paper investigates the intricate energy distribution patterns emerging at an orthotropic piezothermoelastic half-space interface by considering the influence of a higher-order three-phase lags heat conduction law, accompanied by memory-dependent derivatives (referred to as HPS) within the underlying thermoelastic half-space (referred to as TS). This study explores the amplitude and energy ratios of reflected and transmitted waves. These waves span various incident types, including longitudinal, thermal, and transversal, as they propagate through the TS and interact at the interface. Upon encountering the interface, an intriguing dynamic unfolds: three waves experience reflection within the TS medium, while four waves undergo transmission into the HPS medium. A graphical representation effectively illustrates the impact of higher-order time differential parameters and memory to offer comprehensive insights. This visual representation reveals the nuanced fluctuations of energy ratios with the incidence angle. The model astutely captures diverse scenarios, showcasing its ability to interpret complex interface dynamics.
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