scholarly journals A New Fractional Model for Cancer Therapy with M1 Oncolytic Virus

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Majda El Younoussi ◽  
Zakaria Hajhouji ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Mathematical Model ◽  
Cancer Therapy ◽  
Fractional Differential Equations ◽  
Oncolytic Virus ◽  
Equilibrium Points ◽  
Well Posedness ◽  
Boundedness Of Solutions ◽  
Proposed Model ◽  
Fractional Differential ◽  
Theoretical Results

The aim of this work is to propose and analyze a new mathematical model formulated by fractional differential equations (FDEs) that describes the dynamics of oncolytic M1 virotherapy. The well-posedness of the proposed model is proved through existence, uniqueness, nonnegativity, and boundedness of solutions. Furthermore, we study all equilibrium points and conditions needed for their existence. We also analyze the global stability of these equilibrium points and investigate their instability conditions. Finally, we state some numerical simulations in order to exemplify our theoretical results.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

scholarly journals Memory effects on the proliferative function in the cycle-specific of chemotherapy

2021 ◽  
Author(s):  
Najma Ahmed ◽  
Dumitru Vieru ◽  
Fiazud Din Zaman
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Numerical Solutions ◽  
Classical Model ◽  
Cell Mass ◽  
Time Derivative ◽  
Fractional Model ◽  
Fractional Differential ◽  
Mathcad Software

A generalized mathematical model of the breast and ovarian cancer is developed by considering the fractional differential equations with Caputo time-fractional derivatives. The use of the fractional model shows that the time-evolution of the proliferating cell mass, the quiescent cell mass, and the proliferative function are significantly influenced by their history. Even if the classical model, based on the derivative of integer order has been studied in many papers, its analytical solutions are presented in order to make the comparison between the classical model and the fractional model. Using the finite difference method, numerical schemes to the Caputo derivative operator and Riemann-Liouville fractional integral operator are obtained. Numerical solutions to the fractional differential equations of the generalized mathematical model are determined for the chemotherapy scheme based on the function of "on-off" type. Numerical results, obtained with the Mathcad software, are discussed and presented in graphical illustrations. The presence of the fractional order of the time-derivative as a parameter of solutions gives important information regarding the proliferative function, therefore, could give the possible rules for more efficient chemotherapy.

scholarly journals Stability analysis of linear conformable fractional differential equations system with time delays

2019 ◽  
Vol 38 (6) ◽  
pp. 159-171 ◽  
Author(s):  
Vahid Mohammadnezhad ◽  
Mostafa Eslami ◽  
Hadi Rezazadeh
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Euler’S Method ◽  
Fractional Differential ◽  
Theoretical Results

In this paper, we first study stability analysis of linear conformable fractional differential equations system with time delays. Some sufficient conditions on the asymptotic stability for these systems are proposed by using properties of the fractional Laplace transform and fractional version of final value theorem. Then, we employ conformable Euler’s method to solve conformable fractional differential equations system with time delays to illustrate the effectiveness of our theoretical results

Kinematic and Dynamic Determinations of the Movement of the Car when Moving between Cones

2020 ◽  
Vol 896 ◽  
pp. 163-168
Author(s):  
Robert Emil Simniceanu ◽  
Dumitru Neagoe ◽  
Mario Trotea ◽  
Augustin Constantinescu
Keyword(s):  
Mathematical Model ◽  
Mechanical Model ◽  
Experimental Results ◽  
Dynamic Parameters ◽  
Proposed Model ◽  
Theoretical Results

In this paper a mechanical model of the car and the related mathematical model are presented. Based on this mathematical model, some kinematic and dynamic parameters of the car are determined when moving between milestones. These theoretical results are compared with the experimental results to validate the proposed model.

scholarly journals On the solution of two-sided fractional ordinary differential equations of Caputo type

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Ma. Elena Hernández-Hernández ◽  
Vassili N. Kolokoltsov
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Well Posedness ◽  
Solutions To Equations ◽  
Fractional Differential ◽  
The Right ◽  
Stochastic Representations ◽  
Exit Problems ◽  
Special Case

AbstractThis paper provides well-posedness results and stochastic representations for the solutions to equations involving both the right- and the left-sided generalized operators of Caputo type. As a special case, these results show the interplay between two-sided fractional differential equations and two-sided exit problems for certain Lévy processes.

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