مشخصات پژوهش

The presence of fractional derivatives and nonlinear terms makes the analytical treatment of nonlinear time-fractional partial differential equations (PDEs) extremely difficult, despite the fact that they are crucial for modeling anomalous diffusion, nonlinear wave propagation, viscoelasticity, fluid flow, and many other processes with memory and hereditary effects. Particularly for lengthy simulations and highly nonlinear cases, classical numerical approaches frequently have low accuracy, high computational costs, or instability. This emphasizes how important it is to create precise, effective techniques that can yield trustworthy results. By building fractional power series solutions with systematic residual corrections, the residual power series method (RPSM) offers a strong semi-analytical framework that enables increased accuracy and convergence without requiring an excessive amount of computing power. By developing a strong and adaptable methodology for resolving nonlinear time-fractional PDEs, this research will advance our theoretical knowledge of fractional models and their real-world applications in science and engineering. ‎