The dynamics of Zika virus with Caputo fractional derivative

Khan, Muhammad Altaf; Ullah, Saif; Farhan, Muhammad

doi:10.3934/math.2019.1.134

Cited by 59 publications

(19 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Additionally, Riemann, Liouville and Euler were interested in this idea. Since then, fractional calculus has suffered an evolution from theory to the real-world applications in medicine, economics and engineering, among others, as they can be modeled by means of differential equations with fractional order derivatives (see, [1][2][3][4], for example).…”

Section: Introductionmentioning

confidence: 99%

“…Iter 0.6x12 8.41 × 10 −9 1.86 × 10 −8 36x 12 1.43 × 10 −7 2.69 × 10 −4 500 -5.36 × 10 −8 9.84 × 10 −5 500 0.65x 12 9.13 × 10 −9 1.65 × 10 −8 24x 13 9.89 × 10 −9 5.28 × 10 .42 × 10 −9 3.02 × 10 −8 63x 13 9.91 × 10 −9 3.05 × 10 −6 121x 4 9.92 × 10 −9 7.47 × 10 −6 224 0.75x12 4.07 × 10 −9 4.28 × 10 −9 10x 12 9.87 × 10 −9 4.51 × 10 −6 235x 12 9.76 × 10 −9 2.65 × 10 −6 142 0.8x 10 9.98 × 10 −9 2.35 × 10 −8 22x 11 9.54 × 10 −9 1.77 × 10 −6 76x 9 9.74 × 10 −9 1.33 × 10 −6 52 0.85x 10 4.76 × 10 −9 8.25 × 10 −9…”

unclassified

See 1 more Smart Citation

Multipoint Fractional Iterative Methods with (2α + 1)th-Order of Convergence for Solving Nonlinear Problems

2020

View full text Add to dashboard Cite

In the recent literature, some fractional one-point Newton-type methods have been proposed in order to find roots of nonlinear equations using fractional derivatives. In this paper, we introduce a new fractional Newton-type method with order of convergence α + 1 and compare it with the existing fractional Newton method with order 2 α . Moreover, we also introduce a multipoint fractional Traub-type method with order 2 α + 1 and compare its performance with that of its first step. Some numerical tests and analysis of the dependence on the initial estimations are made for each case, including a comparison with classical Newton ( α = 1 of the first step of the class) and classical Traub’s scheme ( α = 1 of fractional proposed multipoint method). In this comparison, some cases are found where classical Newton and Traub’s methods do not converge and the proposed methods do, among other advantages.

show abstract

Section: Introductionmentioning

confidence: 99%

unclassified

Multipoint Fractional Iterative Methods with (2α + 1)th-Order of Convergence for Solving Nonlinear Problems

2020

View full text Add to dashboard Cite

show abstract

“…Since their early development in the XIX-th century until nowadays, fractional calculus has evolved from theoretical aspects to the appearance in many real world applications: mechanical engineering, medicine, economy, and others. They are frequently modeled by differential equations with derivatives of fractional order (see, for example [1][2][3][4] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

A Variant of Chebyshev’s Method with 3αth-Order of Convergence by Using Fractional Derivatives

2019

View full text Add to dashboard Cite

In this manuscript, we propose several iterative methods for solving nonlinear equations whose common origin is the classical Chebyshev’s method, using fractional derivatives in their iterative expressions. Due to the symmetric duality of left and right derivatives, we work with right-hand side Caputo and Riemann–Liouville fractional derivatives. To increase as much as possible the order of convergence of the iterative scheme, some improvements are made, resulting in one of them being of 3 α -th order. Some numerical examples are provided, along with an study of the dependence on initial estimations on several test problems. This results in a robust performance for values of α close to one and almost any initial estimation.

show abstract

“…A new derivative with exponential kernel is proposed in [3]. Some new recent work regarding the fractional derivative and their applications to models arising science and engineering are documented in [12,5,11,17,22]. A fractional derivative and its application to some linear and nonlinear chaotic system is considered in [12].…”

mentioning

confidence: 99%

“…Application of the chaos synchronization within the scope of fractional derivative is proposed in [5]. A Zika virus model and its dynamics in fractional derivative is investigated in [11]. The oxygen diffusion equations and their application to capillary tissues with the use of fractional derivative are discussed in [17].…”

mentioning

confidence: 99%

Application of Caputo-Fabrizio derivative to a cancer model with unknown parameters

El-Dessoky¹,

Khan²

2021

DCDS-S

View full text Add to dashboard Cite

The present work explores the dynamics of a cancer model with fractional derivative. The model is formulated in fractional type of Caputo-Fabrizio derivative. We analyze the chaotic behavior of the proposed model with suggested parameters. Stability results for the fixed points are shown. A numerical scheme is implemented to obtain the graphical results in the sense of Caputo-Fabrizio derivative with various values of the fractional order parameter. Further, we show the graphical results in order to study that the model behaves the periodic and quasi periodic limit cycles as well as chaotic behavior for the given set of parameters.

show abstract

The dynamics of Zika virus with Caputo fractional derivative

Cited by 59 publications

References 10 publications

Multipoint Fractional Iterative Methods with (2α + 1)th-Order of Convergence for Solving Nonlinear Problems

Multipoint Fractional Iterative Methods with (2α + 1)th-Order of Convergence for Solving Nonlinear Problems

A Variant of Chebyshev’s Method with 3αth-Order of Convergence by Using Fractional Derivatives

Application of Caputo-Fabrizio derivative to a cancer model with unknown parameters

Contact Info

Product

Resources

About