Optimal chemotherapy and immunotherapy schedules for a cancer‐obesity model with Caputo time fractional derivative

Yıldız, Tuğba Akman; Arshad, Sadia; Băleanu, Dumitru

doi:10.1002/mma.5298

Cited by 22 publications

(7 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Additionally, optimal control has been explored in fractional cancer treatment models (Akman Yıldız et al. 2018 ; Sweilam et al. 2020 ; Baleanu et al.…”

Section: Introductionmentioning

confidence: 99%

“…And in Morales-Delgado et al (2019), the Caputo-Fabrizio and Atangana-Baleanu definitions were used in a model of cancer chemotherapy, wherein the time history captured new dynamics of the chemotherapy treatment. Additionally, optimal control has been explored in fractional cancer treatment models (Akman Yıldız et al 2018;Sweilam et al 2020;Baleanu et al 2019).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modelling Radiation Cancer Treatment with a Death-Rate Term in Ordinary and Fractional Differential Equations

et al. 2023

View full text Add to dashboard Cite

Fractional calculus has recently been applied to the mathematical modelling of tumour growth, but its use introduces complexities that may not be warranted. Mathematical modelling with differential equations is a standard approach to study and predict treatment outcomes for population-level and patient-specific responses. Here, we use patient data of radiation-treated tumours to discuss the benefits and limitations of introducing fractional derivatives into three standard models of tumour growth. The fractional derivative introduces a history-dependence into the growth function, which requires a continuous death-rate term for radiation treatment. This newly proposed radiation-induced death-rate term improves computational efficiency in both ordinary and fractional derivative models. This computational speed-up will benefit common simulation tasks such as model parameterization and the construction and running of virtual clinical trials.

show abstract

“…Additionally, optimal control has been explored in fractional cancer treatment models (Akman Yıldız et al. 2018 ; Sweilam et al. 2020 ; Baleanu et al.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling Radiation Cancer Treatment with a Death-Rate Term in Ordinary and Fractional Differential Equations

et al. 2023

View full text Add to dashboard Cite

show abstract

“…[33] Investigates as an optimal control problem the effects of chemotherapy treatment on the growth of tumors, by using a model of tumorimmune surveillance. [34] Models the effects of obesity on cancerous tumors growth with Caputo time fractional derivative, and compares three different treatment strategies: chemotherapy, immunotherapy and their combination. [35] Optimally controls the variables of immunotherapy and anti-angiogenic therapy, to reduce the load of cancer cells with a discrete time-delay.…”

Section: Introductionmentioning

confidence: 99%

Viability control of chemo-immunotherapy and radiotherapy by set-valued analysis

MOUSTAFİD¹

2023

IJIAM

View full text Add to dashboard Cite

In this paper we set-valued analyze the problem of asymptotic stabilizing the tumor size. A mathematical model of exponential tumor growing caused by carcinogenic substance is considered, with chemotherapy, immunotherapy, and radiotherapy effects. We control the model to be viable in therapeutic domains, and reverse the exponential growing of the tumor size. The obtained controls derive from the derivative cone of therapeutic domains as solution of minimizing problem.

show abstract

“…Bahaa [22] has given existance, uniqueness results for a VOFOCP involving Atangana-Baleanu derivative. There are numerous applications of FOCP, for example, in malaria model [23], cancer-obesity model [24], HIV [25], and corona virus [26].…”

Section: Introductionmentioning

confidence: 99%

Legendre wavelet method for solving variable‐order nonlinear fractional optimal control problems with variable‐order fractional Bolza cost

Kumar

Mehra

2022

Asian Journal of Control

View full text Add to dashboard Cite

This paper deals with a numerical method for solving variable‐order fractional optimal control problem with a fractional Bolza cost composed as the aggregate of a standard Mayer cost and a fractional Lagrange cost given by a variable‐order Riemann–Liouville fractional integral. Using the integration by part formula and the calculus of variations, the necessary optimality conditions are derived in terms of two‐point variable‐order boundary value problem. Operational matrices of variable‐order right and left Riemann–Liouville integration are derived, and by using them, the two‐point boundary value problem is reduced into the system of algebraic equations. Additionally, the convergence analysis of the proposed method has been considered. Moreover, illustrative examples are given to demonstrate the applicability of the proposed method.

show abstract

Optimal chemotherapy and immunotherapy schedules for a cancer‐obesity model with Caputo time fractional derivative

Cited by 22 publications

References 38 publications

Modelling Radiation Cancer Treatment with a Death-Rate Term in Ordinary and Fractional Differential Equations

Modelling Radiation Cancer Treatment with a Death-Rate Term in Ordinary and Fractional Differential Equations

Viability control of chemo-immunotherapy and radiotherapy by set-valued analysis

Legendre wavelet method for solving variable‐order nonlinear fractional optimal control problems with variable‐order fractional Bolza cost

Contact Info

Product

Resources

About