Dynamics of pattern formation process in fractional-order super-diffusive processes: a computational approach

Owolabi, Kolade M.; Karaağaç, Berat; Băleanu, Dumitru

doi:10.1007/s00500-021-05885-0

Cited by 17 publications

(6 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent years, fractional calculus has been extensively used to model many phenomena of Physics, Mathematics, and several other branches of Science and Engineering. Some of the recent applications of fractional calculus are References 18‐29.…”

Section: Introductionmentioning

confidence: 99%

Approximation of Caputo‐Prabhakar derivative with application in solving time fractional advection‐diffusion equation

Singh

Sultana

Pandey

2022

Numerical Methods in Fluids

View full text Add to dashboard Cite

This work aims to numerically approximate the Caputo‐Prabhakar derivative and use this approximation for solving the time‐fractional advection‐diffusion equation defined in Caputo‐Prabhakar sense which is widely used in fluid dynamics. In this approach, we approximate the time‐fractional derivative of the mentioned equation by two schemes, namely NS1 and NS2, using linear and quadratic interpolation functions, respectively. The convergence order of the two schemes is 2−α, 3−α, respectively, for 0<α<1. The analytical error bounds for the two schemes are also discussed. Then, these schemes are applied to solve the time‐fractional advection‐diffusion equation defined in the Caputo‐Prabhakar sense numerically. We will prove the solvability and stability of the proposed methods. Numerical examples validate the analytical results. With the reference of an example, we have shown that the schemes work well for the fractional diffusion equation also.

show abstract

Section: Introductionmentioning

confidence: 99%

Approximation of Caputo‐Prabhakar derivative with application in solving time fractional advection‐diffusion equation

Singh

Sultana

Pandey

2022

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…The power law decay [ 18 ] in solution is found with the fractional order of the derivative in contrast to the exponential decay in arbitrary Brownian motion. Therefore, to examine a more realistic model, the integer model is changed to a non-integer order model using the ABC derivative [ 65 , 66 , 69 ] as follows: with the initial conditions, Here, is the quarantined rate of the exposed population, is the disease-induced rate of death, is susceptible quarantined, is quarantined susceptible exposed population, is the probability of symptomatic infected. are constants.…”

Section: Model Descriptionmentioning

confidence: 99%

Numerical analysis of fractional coronavirus model with Atangana-Baleanu derivative in Liouville-Caputo sense

2022

View full text Add to dashboard Cite

The novel coronavirus which emerged at the end of the year 2019 has made a huge impact on the population in all parts of the world. The causes of the outbreak of this deadliest virus in human beings are not yet known to the full extent. In this paper, an investigation is carried out for a new convergent solution of the time-fractional coronavirus model and a reliable homotopy perturbation transform method (HPTM) is used to explore the possible solution. In the presented model, the Atangana-Baleanu derivative in the Liouville-Caputo sense is used. The variations of the susceptible, the exposed, the infected, the quarantined susceptible (isolated and exposed), the hospitalized and the recovered population with time are presented through figures and are further discussed. The effects of selected parameters on the population with the time are also shown through figures. The convergence of solution by the HPTM is shown through tables. The results reveal that the HPTM is efficient, systematic, very effective, and easy to use in getting a solution to this new time-fractional mathematical model of coronavirus disease.

show abstract

“…Note also that such Atangana-Baleanu fractional derivative has been applied, cited, and studied in many research areas ranged from electrical engineering to epidemiology. 27,[31][32][33][34][35][36][37][38][39][40][41][42][43][44] In particular, we choose the Atangana-Baleanu fractional derivative in Liouville-Caputo sense rather than the derivative in Riemann-Liouville sense. This is because the former takes the initial condition into its Laplace transformation, 30,33 and we solve the fractional-order memristor's state equation of by means of the Laplace transformation-based methodology.…”

Section: Introductionmentioning

confidence: 99%

“…Between two well‐known nonsingular kernel fractional derivatives, i.e., the Caputo‐Fabrizio fractional derivative 29 and the Atangana‐Baleanu fractional derivative 30 ; we choose the latter as it is a generalization of the former and also nonlocal. Note also that such Atangana‐Baleanu fractional derivative has been applied, cited, and studied in many research areas ranged from electrical engineering to epidemiology 27,31–44 . In particular, we choose the Atangana‐Baleanu fractional derivative in Liouville‐Caputo sense rather than the derivative in Riemann‐Liouville sense.…”

Section: Introductionmentioning

confidence: 99%

A novel generalized fractional‐order memristor model with fully explicit memory description

Banchuin

2022

Circuit Theory & Apps

View full text Add to dashboard Cite

In this work, a novel generalized mathematical model of fractional‐order memristor with fully explicit memory description has been proposed. For obtaining such full explicit memory description, the Atangana‐Baleanu fractional derivative in Liouville‐Caputo sense, which employs a nonsingular kernel, has been adopted as the mathematical basis. The proposed model has been derived without regarding to any specific conventional memristor. A comparison with the singular kernel fractional derivative‐based model has been made. The behavioral analysis of the fractional‐order memristor based on the proposed model has been performed, where both DC and AC stimuli have been considered. In addition, its application to the practical fractional‐order memristor‐based circuit and its extension to the fractional‐order memreactance have also been shown. Unlike the singular kernel fractional derivative‐based model, a fully explicit memory description can be obtained by ours. Many other interesting results that are contradict to the previous singular kernel fractional derivative‐based ones, e.g., the fractional‐order memristor that can be locally active, have been demonstrated. The abovementioned extension can be conveniently performed. In summary, this is the first time that a nonsingular kernel fractional derivative has been applied to the fractional‐order memristor modeling and the resulting model with a fully explicit memory description has been proposed. The proposed model is also highly generic, applicable to the practical circuit, and extendable to the fractional‐order memreactance.

show abstract

Dynamics of pattern formation process in fractional-order super-diffusive processes: a computational approach

Cited by 17 publications

References 61 publications

Approximation of Caputo‐Prabhakar derivative with application in solving time fractional advection‐diffusion equation

Approximation of Caputo‐Prabhakar derivative with application in solving time fractional advection‐diffusion equation

Numerical analysis of fractional coronavirus model with Atangana-Baleanu derivative in Liouville-Caputo sense

A novel generalized fractional‐order memristor model with fully explicit memory description

Contact Info

Product

Resources

About