Work

An Efficient Wavelet Technique for Solving Variable-order Fractional Equations Arising in Contaminant Transport Through Porous Media

Year: 2025

Type: article

Abstract: 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 [Formula: see text] and the Riemann–Liouville (R-L) variable space fractional derivatives [Formula: see text] and [Formula: see text]. 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.

Source: Fractals

DOI: 10.1142/s0218348x25402388

Authors: SHAH JAHAN, POOJA YADAV, KAMAL SHAH, THABET ABDELJAWAD

Institutions: Central University of Haryana, Prince Sultan University, Gulf University for Science & Technology, China Medical University, Sefako Makgatho Health Sciences University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4412594246

FWCI: 3.058

Cites: 53

Cited by: 4

Related to: 10