Stability analysis and new solitary wave solutions for density-dependent space time fractional reaction–diffusion equation

This manuscript offers a thorough investigation into the density-dependent space–time fractional reaction–diffusion equation with conformable derivatives. By employing wave transformation, we convert nonlinear partial differential equation equations into nonlinear ordinary differential equations, allowing us to apply analytical methods effectively. One of the significant contributions of this study is the introduction of innovative and efficient techniques for solving the nonlinear density-dependent reaction–diffusion equation. Using the modified Khater method, we derive new exact solutions for these nonlinear fractional equations, encompassing a wide range of solutions such as kink, anti-kink, periodic, dark, and bright singular solutions. To enhance understanding and enable a comparative analysis for different values of α, we provide graphical representations for selected unknown parameter values, illustrating the dynamics and behavior of both the real and imaginary parts of the solutions. Computational analyses were conducted using Mathematica software, showcasing the practical applicability and effectiveness of our proposed approach in addressing multi-dimensional fractional PDE models commonly encountered in the physical sciences. This work not only contributes to advancing theoretical frameworks but also holds significant implications for diverse applications spanning electromagnetic phenomena, fluid dynamics, plasma physics, electrochemistry, laser diodes, optical absorption, and mathematical biology.