Numerical Investigation of the Time Fractional Mobile-Immobile Advection-Dispersion Model Arising from Solute Transport in Porous Media

The generalized equal width model is an important non-linear dispersive wave model which is naturally used to describe physical situations in a water channel. In this work, we implement the idea of the interpolation by radial basis function to obtain numerical solution of the non-linear time fractional generalized equal width model defined by Caputo sense. In this technique, firstly, a time discretization is accomplished via the finite difference approach and the non-linear term is linearized by a linearization method. Afterwards, with the help of the radial basis function approximation method is used to discretize the spatial derivative terms. The stability of the method is theoretically discussed using the von Neumann (Fourier series) method. Numerical results and comparisons are presented which illustrate the validity and accuracy of our proposed concepts.

show abstract

“…Inspired by [20], the approximation of temporal fractional derivative term appearing in eq. (1) was discretized:…”

Section: Time Discretization Strategymentioning

confidence: 99%

“…Since phenomena can be described more accurately via fractional derivative. Due to this reasons, the analytical and numerical methods have increasingly been used to solve fractional models, see [10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Numerical computation of the time non-linear fractional generalized equal width model arising in shallow water channel

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…The derivatives and integrals of arbitrary order are very convenient for describing properties of many real-world physical systems, and the new fractional models are more satisfying than former integer-order ones (Kilbas et al 2006;Podlubny 1999;Samko et al 1993). In this sense, with the growing developments in the various fields of science and engineering (Debnath 2003;Ansari 2016, 2017;Eshaghi et al 2019Eshaghi et al , 2020Esmaeelzade et al 2020;Golbabai et al 2019;Mainardi 1994Mainardi , 1997Metzler et al 1995;Nikan et al 2020a, b), the concepts of stability analysis of the fractional differential systems have attracted increasing interest for many researchers. For example, some authors studied the stability of fractional order nonlinear systems with the Caputo derivative by using the Lyapunov direct method with the concept of the Mittag-Leffler stability (Li and Chen 2010;Liu et al 2016;Zhang et al 2011).…”

Section: Introductionmentioning

confidence: 99%

Stability and dynamics of neutral and integro-differential regularized Prabhakar fractional differential systems

2020

View full text Add to dashboard Cite

In this work, we investigate the asymptotic stability analysis for two classes of nonlinear fractional systems with the regularized Prabhakar derivative. The stability analysis of the neutral and integro-differential nonlinear fractional systems are studied by assessing the eigenvalues of associated matrix and applying conditions on the nonlinear part of these types of systems. We use a numerical method to solve the fractional differential equations with the regularized Prabhakar fractional derivative. We further present the numerical simulations on several test cases to examine and reveal the complex dynamics of the analytical obtained results.

show abstract

“…It is worth to mention that the main characteristic of the trajectory of the fractional order derivatives is non-local as the memory effect [20]. Many authors derived that fractional differential equations (FDEs) are more suitable than integer order ones, because fractional derivatives describe the memory and hereditary properties of diverse materials and processes [12,13,17,8]. Recently, FDEs have gained much interest in many research areas such as engineering, physics, chemistry, economics, and other branches of science [20,25,7,17,8,16].…”

mentioning

confidence: 99%

Numerical simulation of the nonlinear fractional regularized long-wave model arising in ion acoustic plasma waves

Nikan¹,

Molavi-Arabshai²,

Jafari³

2021

DCDS-S

Self Cite

View full text Add to dashboard Cite

This paper aimed at obtaining the traveling-wave solution of the nonlinear time fractional regularized long-wave equation. In this approach, firstly, the time fractional derivative is accomplished using a finite difference with convergence order O(δt 2−α) for 0 < α < 1 and the nonlinear term is linearized by a linearization technique. Then, the spatial terms are approximated with the help of the radial basis function (RBF). Numerical stability of the method is analyzed by applying the Von-Neumann linear stability analysis. Three invariant quantities corresponding to mass, momentum and energy are evaluated for further validation. Numerical results demonstrate the accuracy and validity of the proposed method.

show abstract

Numerical Investigation of the Time Fractional Mobile-Immobile Advection-Dispersion Model Arising from Solute Transport in Porous Media

Cited by 35 publications

References 48 publications

Numerical computation of the time non-linear fractional generalized equal width model arising in shallow water channel

Numerical computation of the time non-linear fractional generalized equal width model arising in shallow water channel

Stability and dynamics of neutral and integro-differential regularized Prabhakar fractional differential systems

Numerical simulation of the nonlinear fractional regularized long-wave model arising in ion acoustic plasma waves

Contact Info

Product

Resources

About