A Novel Definition of the Caputo Fractional Finite Difference Approach for Maxwell Fluid

This paper investigates the modeling and analysis of a nonlinear fractional Maxwell fluid flowing over a vertical plate using a newly proposed definition of the Caputo fractional derivative. The proposed formulation is specifically designed for efficient implementation within the finite difference method. Buoyancy and magnetic field effects are incorporated to represent realistic physical conditions better. The model is examined through both theoretical analysis and numerical simulations over specified ranges of the fractional parameters, and several important theorems are established. A comparative simulation study is conducted to evaluate the accuracy of different fractional derivative operators. The proposed definition exhibits a high convergence rate and reduced computational cost, meeting the primary objectives of the study. Graphical results further illustrate the influence of key physical parameters on velocity and temperature distributions.