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

This project presents a new mathematical definition of the Caputo fractional derivative designed specifically for the finite difference method. The study models a nonlinear fractional Maxwell fluid flowing along a vertical plate while incorporating buoyancy effects, making the model more realistic with respect to magnetic field interactions.

The newly formulated fractional derivative is implemented and analyzed through both theoretical proofs and numerical simulations. The model investigates the fractional parameters α∈(0,1) and β∈(0,1), demonstrating how variation in these parameters influences the physical behavior.