A Meshfree Approach for Solving Fractional Galilei Invariant Advection–Diffusion Equation through Weighted–Shifted Grünwald Operator

Fractional Galilei invariant advection–diffusion (GIADE) equation, along with its more general version that is the GIADE equation nonlinear source term, discretized by coupling weighted and shifted Grünwald difference approximation formulae Crank–Nicolson technique. The new of backward substitution method, a well-established class meshfree methods, proposed for numerical consequent equation. In present approach, final given summation radial basis functions, primary approximation, related correcting functions. Then, substituted back to governing equations where unknown parameters can be determined. polynomials, trigonometric multiquadric, or Gaussian functions are used in GIADE. Moreover, quasilinearization technique employed transform term into linear term. Finally, three experiments one two dimensions presented support method.