A Legendre Approximation for Solving a Fuzzy Fractional Drug Transduction Model into the Bloodstream

Ahmadian, Ali; Senu, Norazak; Larki, Farhad; Salahshour, Soheil; Suleiman, Mohamed; Islam, Md. Shabiul

doi:10.1007/978-3-319-07692-8_3

Cited by 12 publications

(3 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To this end, they exploited generalized H-differentiability and derived the solutions based on this concept. Ahmadian et al [22] were confined with the application of Legendre operational matrix for solving FFDEs arising in the drug delivery model into the bloodstream. The main motivation of this research is to recommend a suitable way to approximate fuzzy fractional pharmacokinetics-pharmacodynamic models using a shifted Legendre tau approach.…”

Section: Introductionmentioning

confidence: 99%

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

Agarwal

Băleanu

Nieto

et al. 2018

Journal of Computational and Applied Mathematics

149

View full text Add to dashboard Cite

We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.

show abstract

Section: Introductionmentioning

confidence: 99%

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

Agarwal

Băleanu

Nieto

et al. 2018

Journal of Computational and Applied Mathematics

149

View full text Add to dashboard Cite

show abstract

“…The new well-known numerical scheme, like the non-standard finite difference scheme In the end, we could extend this idea to all types of nonlinear and complex models. In the future, we could develop our analysis into fuzzy epidemic models and many other types of modeling as given in [27][28][29][30][31].…”

Section: Discussionmentioning

confidence: 99%

Computational Approximations for Real-World Application of Epidemic Model

Alsallami¹,

Raza²,

Elmahi³

et al. 2022

Intelligent Automation &Amp; Soft Computing

View full text Add to dashboard Cite

The real-world applications and analysis have a significant role in the scientific literature. For instance, mathematical modeling, computer graphics, camera, operating system, Java, disk encryption, web, streaming, and many more are the applications of real-world problems. In this case, we consider disease modeling and its computational treatment. Computational approximations have a significant role in different sciences such as behavioral, social, physical, and biological sciences. But the well-known techniques that are widely used in the literature have many problems. These methods are not consistent with the physical nature and even violate the actual behavior of the continuous model. The structural properties needed for such disciplines, as dynamical consistency, positivity, and boundedness, are the critical requirements of the models in these fields. We studied the transmission of Lassa fever dynamically and numerically. The model's positivity, boundedness, reproduction number, equilibria, and local stability are investigated in dynamical analysis. In numerical analysis, we developed some explicit and implicit methods. Unfortunately, explicit methods like Euler and Runge Kutta are time-dependent and violate the physical properties of the disease. Then, the proposed implicit method for the said model, the non-standard finite difference, is independent of the time step, dynamically consistent, positive, and bounded. In the end, a comparison of methods is presented.

show abstract

“…Ahmadian et al 18 proposed a Jacobi tau method to simulate the concentration of drug in blood for the fuzzy fractional pharmacokinetics. And then in order to solve the fuzzy fractional differential equation arising in the drug delivery model, Ahmadian et al 19 also gave a numerical method based on Legendre operational matrix. Dokoumetzidis et al applied the numerical inverse Laplace transform (NILT) method to solve the system they proposed, 14 but the direct numerical simulation of the two‐compartmental fractional model was not considered in their studies.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of a two‐compartmental fractional model in pharmacokinetics and parameters estimation

Qiao

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

Compartmental model is the classic and widely used approach in pharmacokinetics. Recently, fractional calculus is introduced to describe the time course of drugs in human body which follow the anomalous diffusion mechanism. To consider the different fractional order transmission process, the two‐compartmental fractional model has been proposed and studied. And it will be of great significance to find out a simple and efficient numerical method to solve the model and estimate model parameters. This work investigates two numerical methods of the two‐compartmental fractional model using finite difference schemes, which are based on the shifted Grünwald–Letnikov approximate formula and L1 formula, respectively. The hybrid Nelder–Mead simplex search and particle swarm optimization, denoted as NMSS–PSO, is provided to estimate the fractional model parameters. Comparison between the numerical solution and the solution by the numerical inverse Laplace transform method establishes the validity of the developed numerical algorithms. Then the influence of the order of fractional derivative on the drug amount in human body is also discussed. Finally, the two‐compartmental fractional model is applied to fit the amiodarone pharmacokinetics data based on the NMSS–PSO algorithms. This work will be of importance for the development of fractional pharmacokinetics.

show abstract

A Legendre Approximation for Solving a Fuzzy Fractional Drug Transduction Model into the Bloodstream

Cited by 12 publications

References 36 publications

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

Computational Approximations for Real-World Application of Epidemic Model

Numerical simulation of a two‐compartmental fractional model in pharmacokinetics and parameters estimation

Contact Info

Product

Resources

About