Bell Wavelet operational matrix method for convection diffusion equation

In this article, we introduce an efficient method using Bell wavelets to solve fractional-order convection-diffusion equations with variable coefficients and initial-boundary conditions.We begin by integrating block pulse functions with the Bell wavelet matrix to construct the fractional-order operational matrix of integration (OMI).This method simplifies fractional models by converting them into a set of algebraic equations via the collocation technique.The Bell wavelet collocation technique results in an efficient computational approach characterised by low costs and rapid convergence.Four numerical examples are presented, and the results are compared with exact solutions and other existing methods to validate the method and demonstrate its effectiveness and applicability.Graphical results highlight significant variations between fractional and integer orders, while our method adeptly handles both initial and boundary conditions, enhancing overall accuracy and simple applicability.