Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

Farman, Muhammad; Akgül, Ali; Ahmad, Aqeel; Imtiaz, Sumiyah

doi:10.1002/mma.6240

Cited by 26 publications

(22 citation statements)

References 36 publications

(57 reference statements)

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“…In coming days, it is a motivation for those mechanisms which help for the development of fractional calculus and its applications in various fields of science. [27][28][29][30][31][32][33][34][35] This paper certifies the application of new analytical approach called EDAM [36][37][38] to secure soliton solutions of Newel-Whitehead-Segel (NWS) equation and Zeldovich equation (ZE). [39][40][41] NWS equation is an significant nonlinear reaction-diffusion equation commonly used in biology, circuit theory, population genetics and used to model the transmission of nerve impulse, while ZE is described to arise in combustion theory.…”

Section: Introductionmentioning

confidence: 84%

On solutions of the Newell–Whitehead–Segel equation and Zeldovich equation

Rehman

Asjad

Ullah

et al. 2021

Math Methods in App Sciences

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In this study, we present new solutions of Newel-Whitehead-Segel and Zeldovich equations via the new extended direct algebraic method (EDAM) by taking the special values to involved parameters in the method. The novel exact and soliton solutions are extracted in form of generalized trigonometric and hyperbolic functions. These acquired results reveal the supremacy of the new EDAM. For more illustration of our retrieved solutions, some distinct kinds of 2D and 3D graphs are presented.

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Section: Introductionmentioning

confidence: 84%

On solutions of the Newell–Whitehead–Segel equation and Zeldovich equation

Rehman

Asjad

Ullah

et al. 2021

Math Methods in App Sciences

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“…We have presented some basic definitions which has used in proposed work [65–69]. Definition The Riemann‐Liouville (RL) integral operator of order α is characterize as

I_{t}^{α} ϒ false(t false) = \{\begin{matrix} leftlmatrix \\ \frac{1}{Γ false(α false)} \int_{0}^{t} \frac{ϒ false(τ false)}{{false(t - τ false)}^{1 - α}} italicd τ = \frac{1}{Γ false(α false)} t^{α - 1} * ϒ false(t false), α > 0, t > 0, \\ ϒ false(t false), α = 0, \end{matrix}

where t α − 1 *ϒ( t ) is the convolution product of two functions t α − 1 and ϒ( t ). Definition The fractional derivative of order α in the sense of Caputo's is characterize as

_{0}^{C} D_{t}^{α} ϒ false(t false) = \{\frac{1}{Γ false(n - α false)} \int_{0}^{t} \frac{{normalϒ}^{(n)} false(τ false)}{{false(t - τ false)}^{α + 1 - n}} italicd τ, n - 1 < α \leq n, n \in N .

…”

Section: Preliminariesmentioning

confidence: 99%

A wavelet based numerical scheme for fractional order SEIR epidemic of measles by using Genocchi polynomials

Kumar

Osman

et al. 2020

Numerical Methods Partial

156

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Epidemiology is the glorious discipline underlying medical research, public health practice, and health care evaluation. Nowadays, research on disease models with anonymous parameters is a popular issue for researchers working in epidemiology. Due to popularity of this field, a new numerical method for the solution of the fractional SEIR epidemic of measles is introduced where fractional derivative is taken in Caputo sense. We have discussed about the framework of Genocchi wavelets for numerical simulations of above disease model. Furthermore, the operational matrix merged with the collocation method is used in order to convert fractional‐order problem into algebraic equations. The Adams‐Bashforth‐Moulton (ABM) numerical scheme is used to solve above disease model with various parameters. For we have compared the solutions with Adams‐Bashforth‐Moulton predictor corrector scheme for the accuracy and applicability of the Genocchi wavelets method (GWM). The behaviors of susceptible, exposed, infected, and recovered individuals are presented graphically at the value of various fractional order. The error and convergence analysis of the Genocchi wavelets has been discussed for the applicability of the present methods. Further, various numerical simulations have been carried out to justify our achieved finding.

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“…The idea of fractional derivative is introduced by Riemann Liouville which is based on power law. The new fractional derivative which is applying the exponential‐decay kernel is proposed by Caputo and Fabrizio 12 after Caputo–Frabrizio 13–16 represents non‐singular kernel fractional derivative which includes the trigonometric and exponential function, and the literature 17–25 shows some related approaches for models of epidemic. The proposed outbreak of this virus effectively catches the time line for the COVID‐19 disease conceptual model 26–28 .…”

Section: Introductionmentioning

confidence: 99%

Modeling of fractional‐order COVID‐19 epidemic model with quarantine and social distancing

Farman

Aslam

Akgül

et al. 2021

Math Methods in App Sciences

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Different countries of the world are facing a serious pandemic of corona virus disease (COVID‐19). One of the most typical treatments for COVID‐19 is social distancing, which includes lockdown; it will help to decrease the number of contacts for undiagnosed individuals. The main aim of this article is to construct and evaluate a fractional‐order COVID‐19 epidemic model with quarantine and social distancing. Laplace homotopy analysis method is used for a system of fractional differential equation (FDEs) with Caputo and Atangana–Baleanu–Caputo (ABC) fractional derivative. By applying the ABC and Caputo derivative, the numerical solution for fractional‐order COVID‐19 epidemic model is achieved. The uniqueness and existence of the solution is checked by Picard–Lindelof's method. The proposed fractional model is demonstrated by numerical simulation which is useful for the government to control the spread of disease in a practical way.

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Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

Cited by 26 publications

References 36 publications

On solutions of the Newell–Whitehead–Segel equation and Zeldovich equation

On solutions of the Newell–Whitehead–Segel equation and Zeldovich equation

A wavelet based numerical scheme for fractional order SEIR epidemic of measles by using Genocchi polynomials

Modeling of fractional‐order COVID‐19 epidemic model with quarantine and social distancing

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