ANALYTICAL AND NUMERICAL INVESTIGATIONS OF SOLITON STRUCTURES IN A TIME-FRACTIONAL (2 + 1)-DIMENSIONAL KONOPELCHENKO–DUBROVSKY SYSTEM

In this work, we present a comprehensive analytical and numerical investigation of soliton solutions for a time-fractional [Formula: see text]-dimensional Konopelchenko–Dubrovsky (KD) system describing multidimensional nonlinear wave propagation with memory effects. The model incorporates a modified Riemann–Liouville (MRL) time-fractional derivative of order [Formula: see text] and accounts for nonlinear interaction, longitudinal and transverse dispersion, and coupling mechanisms. The governing system is [Formula: see text] and by employing a fractional traveling wave transformation, it is reduced to a second-order nonlinear ordinary differential equation (ODE) describing the wave profile. This reduction preserves the essential balance between nonlinearity, dispersion, and fractional temporal effects, providing a solid foundation for constructing exact solutions. Two complementary analytical techniques, the unified method and the Sardar sub-equation method, are applied to derive multiple families of explicit traveling wave solutions. Several distinct classes of soliton structures, including bright, dark, kink-type, singular, and composite waves, are obtained, illustrating the rich solution space of the fractional KD system. A detailed quantitative analysis is conducted to examine the influence of the fractional order [Formula: see text], wave speed, and dispersion parameters on amplitude, localization, and structural behavior of the solutions. Numerical tabulation allows rigorous assessment of how fractional memory effects modify soliton characteristics compared with the classical integer-order case. The results reveal that fractional dynamics significantly enrich the solution structure of the KD system, yielding a broader spectrum of nonlinear wave patterns and demonstrating the robustness, versatility, and mathematical consistency of the proposed analytical framework. This approach offers a reliable foundation for further theoretical and applied investigations of multidimensional fractional nonlinear wave equations arising in geophysics, fluid dynamics, nonlinear optics, and related applied sciences.