Numerical estimation of the fractional advection–dispersion equation under the modified Atangana–Baleanu–Caputo derivative

Abstract

The transport of contaminants is a crucial environmental issue, and accurate modeling of this phenomenon is vital for developing effective strategies for its management. In this study, We introduce a non-integer model of the advection–dispersion problem arising in the transport of contaminants. The used derivative is described in the modified Atangana–Baleanu–Caputo (MABC) sense which is a new definition based on an extension of the Atangana and Baleanu derivatives. We employ discrete Chebyshev polynomials to gain the numerical solution of the considered equation. First, we generate a new operational matrix through discrete Chebyshev polynomials properties and proposed derivative. Next, via discrete Chebyshev polynomials and the operational matrix, we gain an algebraic system whose solutions are easily obtained. Finally, we solve some examples and compare the results with those obtained from other numerical methods to confirm the practicality and accuracy of the suggested scheme.

Keywords

• Fractional advection–dispersion equation
• Modified Atangana–Baleanu–Caputo derivative
• Discrete Chebyshev polynomial
• Operational matrix