Fractional Kuramoto–Sivashinsky equation with power law and stretched Mittag-Leffler kernel

Taneco-Hernández, M.A.; Morales‐Delgado, V. F.; Gómez‐Aguilar, J.F.

doi:10.1016/j.physa.2019.121085

Cited by 28 publications

(15 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, we extend and improve the existing theory and previous works on Lotka-Volterra and related models in population biology to the fractional-like case. Indeed, the recent studies and experiments on fractional systems indicated that fractional models are more effective than integer-order models in numerous applications mainly because of their nonlocal properties [1][2][3][4][5][6][7][8][9][10][11][12][13]. In addition, the FLDs have important advantages in computational aspects than classical fractional derivatives, such as Caputo or Riemann-Liouville types [17][18][19][20][21][22][23][24][25][26][27][28][29], which make them more appropriate for applications.…”

Section: There Exists a Function H(t U) Such Thatmentioning

confidence: 99%

“…See, for example, the books [1][2][3] for basic results of systems with fractional derivatives of Riemann-Liouville and Caputo types. Parallel to the development of the theory of fractional systems, numerous definitions of fractional derivatives have been introduced, such as an Atangana-Baleanu fractional derivative, Hadamard-type fractional derivative, Riesz-Miller derivative, and Chen-Machado derivative, just to mention a few [4][5][6][7][8][9][10][11][12][13]. The papers [14][15][16] offered a comprehensive overview and classifications of different types of fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to h-Manifolds

2019

View full text Add to dashboard Cite

In this paper, an impulsive fractional-like system of differential equations is introduced. The notions of practical stability and boundedness with respect to h-manifolds for fractional-like differential equations are generalized to the impulsive case. For the first time in the literature, Lyapunov-like functions and their derivatives with respect to impulsive fractional-like systems are defined. As an application, an impulsive fractional-like system of Lotka–Volterra equations is considered and new criteria for practical exponential stability are proposed. In addition, the uncertain case is also investigated.

show abstract

Section: There Exists a Function H(t U) Such Thatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to h-Manifolds

2019

View full text Add to dashboard Cite

show abstract

“…We can mention unnumbered studies in this area, and some of them are Yavuz and Özdemir, 19 Kumar et al 20 Ullah et al 21 Singh et al 22 Jajarmi et al 23 Yusuf et al 24 Qureshi et al 25,26 Bas et al 27 Diethelm, 28 and so forth 29–32 . However, we can give some application areas of fractional calculus in the problems of physics and engineering, such as in electrical circuits, 33–35 diffusion, 36,37 fluid mechanics, 38–45 cancer therapy, 46,47 and so on 48–50 …”

Section: Introductionmentioning

confidence: 99%

Microbial survival and growth modeling in frame of nonsingular fractional derivatives

Özarslan

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

In this article, the two‐parameter Weibull model (3) is considered for microbial survival curves by new fractional differential operators to analyze some microbial, common reasons of illnesses, and outbreaks, such as Salmonella spp. cocktail in ground turkey thigh, pork shoulder, and turkey breast at isothermal cooking conditions in 50°C, 54°C, 58°C, 62°C, and 66°C, then Listeria monocytogenes and Escherichia coli O157:H7 are considered in ground beef in the same thermal conditions. Results obtained with nonsingular fractional derivatives, including exponential decay and Mittag‐Leffler kernel, are analyzed comparatively with Caputo fractional and integer‐order derivatives for survival ratio of microbial cells. In the sequel, E. coli O157:H7 in ground beef, Salmonella typhimurium and S. enteritidis in boneless pork chops, and background flora in ground pork and at room temperature, 10°C, 7.2°C, and 4.4°C are considered for microbial growth curves by nonsingular fractional operators, and results obtained are compared with Caputo fractional and integer‐order derivatives. All results for advantage and disadvantage of Atangana‐Baleanu and Caputo‐Fabrizio fractional derivatives are discussed in detail.

show abstract

“…18,19 The Kuramoto-Sivashinsky equation is well defined mathematically and has dynamical properties that have attracted the attention of many researchers. The homotopy and Laplace transform methods have been proposed in Taneco-Hernndez et al 20 for solving the fractional Kuramoto-Sivashinsky equation. The radial basis function approach has been developed in Dehghan and Mohammadi 21 to solve the damped 2D Kuramoto-Sivashinsky equation.…”

Section: Introductionmentioning

confidence: 99%

A numerical method based on the Chebyshev cardinal functions for variable‐order fractional version of the fourth‐order 2D Kuramoto‐Sivashinsky equation

Hosseininia

Heydari

Hooshmandasl

et al. 2020

Math Methods in App Sciences

View full text Add to dashboard Cite

In this article, the variable-order (VO) time fractional 2D Kuramoto-Sivashinsky equation is introduced, and a semidiscrete approach is presented through 2D Chebyshev cardinal functions (CCFs) for solving this equation. In the proposed method, we obtain a recurrent algorithm by using the finite difference method to approximate the VO fractional differentiation, the weighted finite difference method with parameter , and the approximation of the unknown function by the 2D CCFs. The differentiation operational matrices and the collocation technique are used to extract a linear system of algebraic equations which can be easily solved. The credibility of the developed method is examined on three numerical examples.

show abstract

Fractional Kuramoto–Sivashinsky equation with power law and stretched Mittag-Leffler kernel

Cited by 28 publications

References 40 publications

Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to h-Manifolds

Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to h-Manifolds

Microbial survival and growth modeling in frame of nonsingular fractional derivatives

A numerical method based on the Chebyshev cardinal functions for variable‐order fractional version of the fourth‐order 2D Kuramoto‐Sivashinsky equation

Contact Info

Product

Resources

About