Application of the Caputo-Fabrizio and Atangana-Baleanu fractional derivatives to mathematical model of cancer chemotherapy effect

2019 ◽  
Vol 42 (4) ◽  
pp. 1167-1193 ◽  
Author(s):  
Victor Fabian Morales-Delgado ◽  
José Francisco Gómez-Aguilar ◽  
Khaled Saad ◽  
Ricardo Fabricio Escobar Jiménez
Keyword(s):  
Mathematical Model ◽  
Cancer Chemotherapy ◽  
Fractional Derivatives

scholarly journals Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1431
Author(s):  
Bilal Basti ◽  
Nacereddine Hammami ◽  
Imadeddine Berrabah ◽  
Farid Nouioua ◽  
Rabah Djemiat ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Biological Models ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Single Form ◽  
Stability Results

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

Mathematical model of cancer chemotherapy. periodic schedules of phase-specific cytotoxic-agent administration increasing the selectivty of therapy

1985 ◽  
Vol 73 (1) ◽  
pp. 1-31 ◽  
Author(s):  
B.F. Dibrov ◽  
A.M. Zhabotinsky ◽  
Yu.A. Neyfakh ◽  
M.P. Orlova ◽  
L.I. Churikova
Keyword(s):  
Mathematical Model ◽  
Cancer Chemotherapy ◽  
Cytotoxic Agent

Generalized solutions of an equation with fractional derivatives

2009 ◽  
Vol 20 (2) ◽  
pp. 215-229
Author(s):  
B. STANKOVIC ◽  
T. M. ATANACKOVIC
Keyword(s):  
Mathematical Model ◽  
Fractional Derivatives ◽  
Variational Problems ◽  
Generalized Solutions ◽  
Singular Solutions ◽  
Space Of Distributions ◽  
Left And Right

We consider an equation with left and right fractional derivatives which appears as a mathematical model in the mechanics. The type of equations that we analyse appear, as a rule, in variational problems containing fractional derivatives. We look for solutions in a suitably defined sub-space of distributions which is sufficient to enclose different ‘singular’ solutions.

A mathematical model of cancer chemotherapy with an optimal selection of parameters

1990 ◽  
Vol 99 (2) ◽  
pp. 205-230 ◽  
Author(s):  
R.B. Martin ◽  
M.E. Fisher ◽  
R.F. Minchin ◽  
K.L. Teo
Keyword(s):  
Mathematical Model ◽  
Cancer Chemotherapy ◽  
Optimal Selection ◽  
Selection Of

scholarly journals Optimal control for a mathematical model for chemotherapy with pharmacometrics

2020 ◽  
Vol 15 ◽  
pp. 69
Author(s):  
Maciej Leszczyński ◽  
Urszula Ledzewicz ◽  
Heinz Schättler
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Cancer Chemotherapy ◽  
Drug Effects ◽  
Optimal Controls ◽  
Angiogenic Therapy ◽  
Single Drug ◽  
Qualitative Changes

An optimal control problem for an abstract mathematical model for cancer chemotherapy is considered. The dynamics is for a single drug and includes pharmacodynamic (PD) and pharmacokinetic (PK) models. The aim is to point out qualitative changes in the structures of optimal controls that occur as these pharmacometric models are varied. This concerns (i) changes in the PD-model for the effectiveness of the drug (e.g., between a linear log-kill term and a non-linear Michaelis-Menten type Emax-model) and (ii) the question how the incorporation of a mathematical model for the pharmacokinetics of the drug effects optimal controls. The general results will be illustrated and discussed in the framework of a mathematical model for anti-angiogenic therapy.

scholarly journals A mathematical model for identifying the fractional derivative parameter and predicting the results for the fluid flow equation in the well

2021 ◽  
pp. 72-79
Author(s):  
Темирхан Султанович Алероев ◽  
Алла Николаевна Хворова
Keyword(s):  
Mathematical Model ◽  
Fractional Derivatives ◽  
Fractured Reservoirs ◽  
Flow Equation ◽  
Oil Fields ◽  
Coefficient Of Determination ◽  
Experimental Measurements ◽  
Steady State Flow ◽  
Fluid Flow Equation ◽  
The Mathematical Model

В данной статье рассматривается идентификации параметров математической модели, основанной на дифференциальном уравнении с дробными производными. С помощью этой модели описывается установившееся течение в скважине в трещинном деформированном пласте. Рассматриваемая модель может быть использована и при разработке нефтяных месторождений с трещиноватыми коллекторами. Идентификация параметра осуществлялась с помощью оптимизации показателя качества адекватности математической модели - коэффициента детерминации. Также была представлена технология прогнозирования результатов давлений, для области, в которой не проводились экспериментальные измерения. Предлагаемая технология сопровождена расчетами. This article discusses the identification of the parameters of a mathematical model based on a differential equation with fractional derivatives. This model is used to describe the steady-state flow in a well in a fractured deformed formation. The considered model can be used in the development of oil fields with fractured reservoirs. The identification of the parameter was carried out by optimizing the quality indicator of the adequacy of the mathematical model the coefficient of determination. The technology for predicting the results of pressures was also presented, for an area in which no experimental measurements were carried out. The proposed technology is accompanied by calculations.

scholarly journals ON BOUNDARY VALUE PROBLEM FOR GENERALIZED ALLER EQUATION

2021 ◽  
Vol 26 (2) ◽  
pp. 7-14
Author(s):  
S. Kh. Gekkieva ◽  
M. M. Karmokov ◽  
M. A. Kerefov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Porous Media ◽  
Fractional Order ◽  
Moisture Transport ◽  
Fractional Derivatives ◽  
Fractal Structure ◽  
Goursat Problem ◽  
Order Equation ◽  
Fluid Filtration

The mathematical models of fluid filtration processes in porous media with a fractal structure and memory are based on differential equations of fractional order in both time and space variables. The dependence of the soil water content can significantly affect the moisture transport in capillary-porous media. The paper investigates the generalized Aller equation widely used in mathematical modeling of the processes related to water table dynamics in view of fractal structure. As a mathematical model of the Aller equation withRiemann Liouville fractional derivatives, a loaded fractional order equation is proposed, and a solution to the Goursat problem has been written out for this model in explicit form.

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