Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative

Shah, Kamal; Alqudah, Manar A.; Jarad, Fahd; Abdeljawad, Thabet

doi:10.1016/j.chaos.2020.109754

Cited by 136 publications

(76 citation statements)

References 18 publications

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“…Here some basic materials are taken from [30][31][32]. Definition 2.1 If x(t) ∈ H 1 (0, τ ) and r ∈ (0, 1], then the ABC derivative is defined using Mittag-Leffler function M κ as follows:…”

Section: Fundamental Resultsmentioning

confidence: 99%

On modeling of coronavirus-19 disease under Mittag-Leffler power law

2020

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This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as $(\mathcal{ABC})$ ( ABC ) . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam–Hyers type are also established. By applying a numerical technique called fractional Adams–Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.

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Section: Fundamental Resultsmentioning

confidence: 99%

On modeling of coronavirus-19 disease under Mittag-Leffler power law

2020

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“…Because finding exact analytical solutions for every differential equation of fractional order is quite a difficult job, the wellknown techniques including homotopy perturbation method, Adomian decomposition method, and many other numerical methods were utilized for the required results (for details, see [27]). As we know, the mentioned techniques were increasingly adopted for ordinary FODEs, but there are very few articles which study decompositions techniques coupled with integral transform for FODEs under CFFD, see [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Existence theory and approximate solution to prey–predator coupled system involving nonsingular kernel type derivative

et al. 2020

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This manuscript considers a nonlinear coupled system under nonsingular kernel type derivative. The considered problem is investigated from two aspects including existence theory and approximate analytical solution. For the concerned qualitative theory, some fixed point results are used. While for approximate solution, the Laplace transform coupled with Adomian method is applied. Finally, by a pertinent example of prey–predator system, we support our results. Some graphical presentations are given using Matlab.

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“…The subject of fractional calculus can be considered as a generalization of the classical integer order calculus (derivative and integration), and due its important role in science and engineering, it has been gaining considerable attention of many authors and researchers [1][2][3][4][5]. The reader who is interested with the field of fractional calculus knows that there are many definitions of a fractional order derivative and they have been used to describe several real-life problems in many fields of sciences; the most important and famous ones are Riemann-Liouville, Grunwald-Letnikov, and Caputo derivatives [1,2,[6][7][8][9][10]. Riemann-Liouville and Caputo use the integral in its construction, particularly the Cauchy integral formula with modifications.…”

Section: Introductionmentioning

confidence: 99%

Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative

Malik

Mohammed

2020

J Egypt Math Soc

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In this paper, we introduce two reliable efficient approximate methods for solving a class of fractional Lane-Emden equations with conformable fractional derivative (CL-M) which are the so-called conformable Homotopy-Adomian decomposition method (CH-A) and conformable residual power series method (CRP). Furthermore, the proposed methods express the solutions of the non-linear cases of the CL-M in terms of fractional convergent series in which its components can be computed in an easy manner. Finally, the results are given by graphs for each case of the CL-M at different values of α in order to demonstrate its accuracy, applicability, and efficiency.

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Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative

Cited by 136 publications

References 18 publications

On modeling of coronavirus-19 disease under Mittag-Leffler power law

On modeling of coronavirus-19 disease under Mittag-Leffler power law

Existence theory and approximate solution to prey–predator coupled system involving nonsingular kernel type derivative

Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative

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