A new numerical computational method for solving nonhomogeneous time-fractional nonlinear parabolic problems in unbounded domains
This paper addresses the numerical solution of nonhomogeneous time-fractional nonlinear parabolic problems defined on unbounded domains, where challenges arise due to temporal nonlocality, nonlinear dynamics, and the infinite spatial extent. To overcome these difficulties, we propose a novel computational framework that transforms the original unbounded domain problem into an equivalent formulation on a bounded domain through the construction of absorbing boundary conditions. Unlike existing approaches that rely on Pad\'e approximations, our method directly utilizes the fundamental properties of fractional derivatives to define these boundaries more accurately. The resulting problem is then discretized using a high-order finite difference scheme, allowing for efficient and precise numerical implementation. Theoretical analysis confirms that the method is stable and ensures controlled computational error. Numerical experiments demonstrate the practical effectiveness of the proposed approach, achieving accurate results with significantly reduced computational cost. This method provides a reliable and efficient tool for modeling diffusion phenomena governed by time-fractional dynamics in unbounded spatial settings.