On the reducibility of a class of almost-periodic linear Hamiltonian systems and its application in Schrödinger equation

Afzal, Muhammad Sohail; Ismaeel, Tariq; Butt, Azhar Iqbal Kashif; Farooq, Zahid; Ahmad, Riaz; Khan, Ilyas

doi:10.3934/math.2023375

Cited by 2 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A well‐designed mathematical model could help us in understanding the disease's transmission mechanism and it may be useful to study disease patterns for eradication of disease effectively. There exist several mathematical models [1–29] designed by researchers with different assumptions to study flow dynamics and to control of corona virus disease. In this section, we design a new mathematical model for the corona virus disease that will explain the disease transmission dynamics reliably.…”

Section: Covid‐19 Model Formulationmentioning

confidence: 99%

“…Mathematical modeling expresses a real-world phenomenon into mathematical equations that illustrates the entire picture and helps in predicting future outcomes [14][15][16][17][18][19][20][21][22][23][24][25]. Since the outbreak of this pandemic, researchers around the world have been designing and formulating different epidemic mathematical models [26][27][28][29] to investigate the dynamical behavior of corona virus disease.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A new design and analysis of optimal control problems arising from COVID‐19 outbreak

Butt

Chamaleen

Imran

et al. 2023

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this manuscript, we append the hospitalization, diagnosed and isolation compartments to the classic SEIR model to design a new COVID‐19 epidemic model. We further subdivide the isolation compartment into asymptomatic infected and symptomatic infected compartments. For validity of the purposed model, we prove the existence of a unique solution and prove the positivity and boundedness of the solution. To study disease dynamics, we compute equilibrium points and the reproduction number . We also investigate the local and global stabilities at both of the equilibrium points. Sensitivity analysis will be performed to observe the effect of transmission parameters on . For optimal control analysis, we design two different optimal control problems by taking different optimal control approaches. Firstly, we add an isolation compartment in the newly designed model, and secondly, three parameters describing non‐pharmaceutical behaviors such as educating people to take precautionary measures, providing intensive medical care with medication, and utilizing resources by government are added in the model. We set up optimality conditions by using Pontryagin's maximum principle and develop computing algorithms to solve the conditions numerically. At the end, numerical solutions will be displayed graphically with discussion.

show abstract

Section: Covid‐19 Model Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new design and analysis of optimal control problems arising from COVID‐19 outbreak

Butt

Chamaleen

Imran

et al. 2023

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

A Dynamic Competition Analysis of Stochastic Fractional Differential Equation Arising in Finance via Pseudospectral Method

Ali

Khan

2023

Mathematics

View full text Add to dashboard Cite

This research focuses on the analysis of the competitive model used in the banking sector based on the stochastic fractional differential equation. For the approximate solution, a pseudospectral technique is utilized for the proposed model based on the stochastic Lotka–Volterra equation using a wide range of fractional order parameters in simulations. Conditions for stable and unstable equilibrium points are provided using the Jacobian. The Lotka–Volterra equation is unstable in the long term and can produce highly fluctuating dynamics, which is also one of the reasons that this equation is used to model the problems arising in finance, where fluctuations are important. For this reason, the conventional analytical and numerical methods are not the best choices. To overcome this difficulty, an automatic procedure is used to solve the resultant algebraic equation after the discretization of the operator. In order to fully use the properties of orthogonal polynomials, the proposed scheme is applied to the equivalent integral form of stochastic fractional differential equations under consideration. This also helps in the analysis of fractional differential equations, which mostly fall in the framework of their integrated form. We demonstrate that this fractional approach may be considered as the best tool to model such real-world data situations with very reasonable accuracy. Our numerical simulations further demonstrate that the use of the fractional Atangana–Baleanu operator approach produces results that are more precise and flexible, allowing individuals or companies to use it with confidence to model such real-world situations. It is shown that our numerical simulation results have a very good agreement with the real data, further showing the efficiency and effectiveness of our numerical scheme for the proposed model.

show abstract

On the reducibility of a class of almost-periodic linear Hamiltonian systems and its application in Schrödinger equation

Cited by 2 publications

References 13 publications

A new design and analysis of optimal control problems arising from COVID‐19 outbreak

A new design and analysis of optimal control problems arising from COVID‐19 outbreak

A Dynamic Competition Analysis of Stochastic Fractional Differential Equation Arising in Finance via Pseudospectral Method

Contact Info

Product

Resources

About