An Effective Computational Framework Based on Re‐Defined Uniform Hyperbolic Polynomial B‐Spline for Solving Time‐Fractional Reaction Diffusion Equation

ABSTRACT

In this study, a robust computational scheme is designed to solve time‐fractional reaction‐diffusion equation involving the Caputo–Fabrizio derivative. The time‐fractional reaction–diffusion equation provides an effective mathematical framework for modeling the temporal evolution of physical processes while incorporating memory effects arising from their past states. The Caputo–Fabrizio fractional derivative in conjunction with the ‐weighted scheme is employed for temporal integration of the considered problem. The redefined uniform hyperbolic polynomial B‐spline, which improves flexibility and accuracy across the computational domain, is designed to discretize the spatial variables. The stability and convergence analyzes of the developed technique are performed to justify the developed technique's the reliability. The developed scheme is applied to three benchmark problems to assess its feasibility and efficiency. The findings obtained through the numerical experiments reveal that the developed scheme provides significantly more accurate results compared to the polynomial B‐spline method, highlighting its robustness and computational efficiency.