Numerical solution of fractional order smoking model via laplace Adomian decomposition method

Haq, Fazal; Shah, Kamal; Rahman, Ghaus ur; Shahzad, Muhammad

doi:10.1016/j.aej.2017.02.015

Cited by 134 publications

(91 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, this method does not depend upon on a parameter like needed for homotopy perturbation method (HPM) and homotopy analysis method (HAM). Although the solutions obtained vis this method are the same as obtained by ADM, for detail see (Haq et al, 2017;Jafari et al, 2011a;Zhu et al, 1998).…”

Section: *Humanmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical behavior of HIV immunology model with non-integer time fractional derivatives

Ashraf

2018

Int. j. adv. appl. sci.

View full text Add to dashboard Cite

This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body. Human immunodeficiency virus infection destroys the body immune system, increases the risk of certain pathologies, damages body organs such as the brain, kidney and heart or cause the death. Unfortunately, this infection disease currently has no cure to control the diseases. We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. The Caputo fractional derivative operator of order ∈ (0,1] is employed to obtain the system of fractional differential equations. The basic reproductive number is derived for a general viral production rate which determines the local stability of the infection free equilibrium. The solution of the time fractional model has been procured by employing Laplace Adomian decomposition method (LADM) and the accuracy of the scheme is presented by convergence analysis Moreover, numerical simulation are performed to study the dynamical behavior of solution of the models. Simulations of different epidemiological classes at the effect of the fractional parameters revealed that most undergoing treatment join the recovered class. The results show the both viral production rate and death rate of infected cells play an important role the disease in the society.

show abstract

Section: *Humanmentioning

confidence: 99%

“…For detailed over view of the topic readers are referred to (Haq et al, 2017;Johnston et al, 2016;Jafari et al, 2011a;2011b).…”

Section: Preliminariesmentioning

confidence: 99%

Dynamical behavior of HIV immunology model with non-integer time fractional derivatives

Ashraf

2018

Int. j. adv. appl. sci.

View full text Add to dashboard Cite

show abstract

“…Arbitrary order derivatives are powerful tools for the discretion of the dynamical behavior of various biomaterial and systems. The most iterating feature of these models is their global (nonlocal) characteristics which do not exist in the classical order models (Haq et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

“…Although the solutions obtained via this method are the same as obtained by ADM, for detail see (Jafari et al, 2011a;2011b;Johnston et al, 2016). It is to be noted that LADM is powerful than standard ADM method (Haq et al, 2017). Kermack and McKendrick (1927) are inventor of the diseases models and played an important role in mathematical epidemiology to describe the transmission dynamics of measles formulate a deterministic and compartmental mathematical model.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of SIR epidemic model with non-integer time fractional derivatives: A mathematical analysis

Ahmad

2018

Int. j. adv. appl. sci.

View full text Add to dashboard Cite

Protection of children from vaccine preventable diseases, such as measles is among primary goal for health worker. Measles is a highly contagious disease that can spread in a population depending on the number of peoples susceptible or infected and also depending on their dynamics in the community. The model monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine. We presented a nonlinear time fractional model of measles in order to understand the outbreaks of this epidemic disease. The Caputo fractional derivative operator of order ∈ (0,1] is employed to obtain the system of fractional differential equations. The numerical solution of the time fractional model has been procured by employing Laplace Adomian decomposition method (LADM), qualitative and sensitivity analysis of the model was performed. Qualitative results shows that the model has endemic equilibrium which locally asymptotically stable for 0 > 1 and otherwise unstable. The convergence analysis and nonnegative solutions are verified for the proposed scheme. Simulation of different epidemiological classes at the effect of fractional parameter revealed that most individuals undergoing treatment join the recovered class. This method proves to be very efficient techniques for solving epidemic model to control infectious disease.

show abstract

“…Zeb in [37] proposed a fractional smoking dynamic model considering adolescent nicotine dependence. In [10], the authors studied the giving up smoking dynamics using a fractional order model; approximate solutions via Laplace Adomian decomposition method were obtained. The multi-step generalized differential transform method was employed in [9] to obtain accurate solutions to a giving up smoking model of fractional order.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel

Morales‐Delgado¹,

Gómez‐Aguilar²,

Taneco-Hernández³

et al. 2018

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

In this paper, we analyze the fractional modeling of the giving up the smoking using the definitions of Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives. Applying the homotopy analysis method and the Laplace transform with polynomial homotopy, the analytical solution of the smoking dynamics has obtained. Furthermore, using an iterative scheme by the Laplace transform, and the Atangana-Baleanu fractional integral, special solutions of the model are obtained. Uniqueness and existence of the solutions by the fixed-point theorem and Picard-Lindelof approach are studied. Finally, some numerical simulations are carried out for illustrating the results obtained.

show abstract

Numerical solution of fractional order smoking model via laplace Adomian decomposition method

Cited by 134 publications

References 19 publications

Dynamical behavior of HIV immunology model with non-integer time fractional derivatives

Dynamical behavior of HIV immunology model with non-integer time fractional derivatives

Dynamical behavior of SIR epidemic model with non-integer time fractional derivatives: A mathematical analysis

Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel

Contact Info

Product

Resources

About