AN EFFICIENT WAVELET TECHNIQUE FOR SOLVING VARIABLE-ORDER FRACTIONAL EQUATIONS ARISING IN CONTAMINANT TRANSPORT THROUGH POROUS MEDIA

An efficient numerical scheme to approximate the variable-order (V-O) space-time fractional advection–dispersion equation (S-TFADE) is given in this study. The equation is derived from the standard advection-dispersion equation by replacing with the Coimbra variable time fractional derivative (0 < λ₁(z) ≤ 1) and the Riemann–Liouville (R-L) variable space fractional derivatives (0 < λ₂(z,t) ≤ 1) and (1 < λ₃(z,t) ≤ 2). To implement the method, a two-dimensional basis using a Fibonacci wavelet is employed to derive a V-O fractional derivative operational matrix (OM). The effectiveness and accuracy of the presented technique are demonstrated through the resolution of different test problems. Comparative analyses against existing algorithms show the good performance of the presented numerical schemes. The presented approach holds significant promise for advancing the comprehension of anomalous transport in various physical systems governed by fractional calculus.