scholarly journals A Fractional Epidemiological Model for Bone Remodeling Process

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Muath Awadalla ◽  
Yves Yannick Yameni Noupoue ◽  
Kinda Abuasbeh
Keyword(s):  
Bone Formation ◽  
Differential Equations ◽  
Fractional Order ◽  
Formation Process ◽  
Differential Model ◽  
Chemical Substances ◽  
Differential Approach ◽  
Fractional Differential ◽  
The Impact ◽  
Calcitonin Secretion

This article focuses on modeling bone formation process using a fractional differential approach, named bones remodeling process. The first goal of the work is to investigate existence and uniqueness of the proposed fractional differential model. The next goal is to investigate how similar is the proposed approach to the method based on system classical differential equations. The dynamical system of equations used is built upon three main parameters. These are chemical substances, namely, calcitonin secretion, osteoclastic and osteoblastic, which are involved in the bone’s formation process. We implement some numerical simulations to graphically show the impact of an arbitrary fractional order of derivative. We finally obtained that modeling bone formation process using fractional differential equations yielded comparable results with those obtained through a system of classical differential equations. Flexibility in the choice of the fractional order of derivative is an advantage as it helps in selecting the best fractional order of derivative.

A Modified System of Nonlinear Fractional-Order Differential Equations in the Study of the Dynamics of Marital Relationships and their Behavioural Features

2020 ◽  
Vol 8 (1) ◽  
pp. 37-56
Author(s):  
Olutunde Samuel Odetunde ◽  
Rasaki Kola Odunaike ◽  
Adetoro Temitope Talabi
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Decomposition Method ◽  
Divorce Rate ◽  
Marital Relationships ◽  
Impact Factors ◽  
Differential Model ◽  
Fractional Order Differential Equations ◽  
Iterative Decomposition ◽  
The Impact

Urbanization and modernization have effects on marital relationships in Nigeria which led to high divorce rate among legitimate couples prompting unstable environment. This situation design and uses scientific means to study the dynamics of marital relationships and their behavioural features to check excesses in marriage and to promote stability. A modified system of nonlinear fractional-order differential equations was used to categorize people of different personalities and different Impact Factors of Memory, using different sets of parameters. The equations predict and interpret the features of the union of different individuals with external circumstance(s). Equations were adapted to a local environment where data collections were carried out to investigate factors affecting marriages. Data collected by the use of questionnaire validate the model. An Iterative Decomposition Method was adopted to solve the fractional system in which fractional derivatives were given in the Caputo sense; the obtained results were interpreted appropriately. The modified model shows the trajectory of the couple from the state of indifference and as the impact factor memory increases it affects their togetherness making the love between them to decay easily. Numerical simulation results were presented to show the effectiveness of the model and the accuracy of the statements established. Keywords: Differential model, dynamical system, impact factors of memory, iterative decomposition method, marital relationship

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 NUMERICAL SOLUTION FOR TIME-FRACTIONAL MURRAY REACTION-DIFFUSION EQUATIONS VIA REDUCED DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Author(s):  
Muhammed Yiğider ◽  
Serkan Okur
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Reaction Diffusion Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Reduced Differential Transform Method ◽  
Time Fractional Differential Equations

In this study, solutions of time-fractional differential equations that emerge from science and engineering have been investigated by employing reduced differential transform method. Initially, the definition of the derivatives with fractional order and their important features are given. Afterwards, by employing the Caputo derivative, reduced differential transform method has been introduced. Finally, the numerical solutions of the fractional order Murray equation have been obtained by utilizing reduced differential transform method and results have been compared through graphs and tables. Keywords: Time-fractional differential equations, Reduced differential transform methods, Murray equations, Caputo fractional derivative.

scholarly journals On Stability of Nonautonomous Perturbed Semilinear Fractional Differential Systems of Order α∈(1,2)

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammed M. Matar ◽  
Esmail S. Abu Skhail
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Protected Area ◽  
Marine Protected Area ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential ◽  
Stability Results

We study the Mittag-Leffler and class-K function stability of fractional differential equations with order α∈(1,2). We also investigate the comparison between two systems with Caputo and Riemann-Liouville derivatives. Two examples related to fractional-order Hopfield neural networks with constant external inputs and a marine protected area model are introduced to illustrate the applicability of stability results.

scholarly journals An Integral Operational Matrix of Fractional-Order Chelyshkov Functions and Its Applications

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1755
Author(s):  
M. S. Al-Sharif ◽  
A. I. Ahmed ◽  
M. S. Salim
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Operational Matrix ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Science And Engineering ◽  
Numerical Examples ◽  
Fractional Differential

Fractional differential equations have been applied to model physical and engineering processes in many fields of science and engineering. This paper adopts the fractional-order Chelyshkov functions (FCHFs) for solving the fractional differential equations. The operational matrices of fractional integral and product for FCHFs are derived. These matrices, together with the spectral collocation method, are used to reduce the fractional differential equation into a system of algebraic equations. The error estimation of the presented method is also studied. Furthermore, numerical examples and comparison with existing results are given to demonstrate the accuracy and applicability of the presented method.

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