Semi-Analytic Solution of a Linear Space-Fractional Diffusion Equation by the Method of Lines

Abstract

The study of space-fractional diffusion equations is important for modelling anomalous diffusion in physics, engineering, and biomedical sciences. In this work, a semi-analytic solution for a linear space-fractional diffusion equation is developed using the method of lines. The spatial fractional derivative is discretized using central finite differences, transforming the problem into a system of ordinary differential equations in time. This system is then solved using the variation of parameters method, yielding a semi-analytic solution. Numerical results and error analysis demonstrate the accuracy and stability of the proposed method, which can be extended to more complex fractional models.