Exploring Nonlinear Fractional (2+1)-Dimensional KP–Burgers Model: Derivation and Ion Acoustic Solitary Wave Solution

The purpose of this study is to conduct a complete examination into the fractional (2+1)-dimensional nonlinear KP-Burgers (KP-B) model in the setting of quantum plasma. The main goal is to present a mathematical explanation and derivation for the fractional (2+1)-dimensional nonlinear KP-B model. We used the reductive perturbation technique to obtain the fractional (2+1)-dimensional ion acoustic solitary wave, which leads to the nonlinear KP-B model. To solve the fractional space-time KP-B model, we used the modified sub-equation technique and the extended hyperbolic function methodology. This methodology covers rational, periodic wave, and hyperbolic function solutions. Ion acoustic waves were explored in relation to the effects of ion pressure and an external electric field. The effects of density and fractional order on the properties of a single solution are examined. The plasma system is defined as an unmagnetized epi plasma system composed of relativistic ions, positrons, and nonextensive electrons that can be found in a range of astrophysical and cosmological environments. The solution variables include electron-positron and ion-electron temperature ratios, electron and positron nonextensivity strength, ion kinematic viscosity, positron concentration, and the weakly relativistic streaming factor. The fractional order and associated plasma properties have a considerable influence on the phase velocity of ion acoustic waves. When the fractional order equals one, the obtained results are consistent with known outcomes. This work makes a substantial contribution to our understanding of nonlinear events in quantum plasmas, particularly ion acoustic waves. It provides a solid approach for solution development and analysis, with implications for a variety of astrophysical and cosmological scenarios.