On the Generalized Mass Transport Equation to the Concept of Variable Fractional Derivative

2014/01/01 by Abdon Atangana, Adem Kılıçman · 1 citation
Mathematics · Engineering · #Fractional Differential Equations Solutions #Numerical methods in engineering #Numerical methods for differential equations #Convergence (economics) #Mathematics #Stability (learning theory) #Integer (computer science) #Variable (mathematics) #Derivative (finance) #Dispersion (optics) #Fractional calculus #Scheme (mathematics) #Mathematical analysis #Applied mathematics #Constant (computer programming) #Physics #Computer science

paper · pdf · doi:10.1155/2014/542809

openalex publication_date 2014/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The hydrodynamic dispersion equation was generalized using the concept of variational order derivative. The modified equation was numerically solved via the Crank‐Nicholson scheme. The stability and convergence of the scheme in this case were presented. The numerical simulations showed that, the modified equation is more reliable in predicting the movement of pollution in the deformable aquifers, than the constant fractional and integer derivatives.

Citations

• Variable-order fractional derivatives and their numerical approximations
• Variable order differential equations with piecewise constant order-function and diffusion with changing modes

Cited by

• Fractional calculus [wikipedia]

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