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Symmetry
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New Trends in Fractional Calculus and Applications in Engineering and...
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New Trends in Fractional Calculus and Applications in Engineering and Infectious Diseases

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (28 February 2022) | Viewed by 10832

Special Issue Editors

Dr. Olaniyi S Iyiola

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Guest Editor
Department of Mathematics, Computer Science and Information Systems, California University of Pennsylvania, PA 15419, USA
Interests: fractional calculus; numerical analysis and methods; fixed point theory and its applications
Prof. Erkan Nane

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Guest Editor
Department of Mathematics and Statistics, Auburn University, Auburn, USA
Interests: probability and its connections to harmonic analysis; partial differential equations; spectral theory and geometry

Special Issue Information

Dear Colleagues,

The need for fractional calculus in science and engineering fields in recent decades has greatly increased. Complex systems with hereditary and memory properties are best modeled using fractional calculus. This is due to the nonlocal nature of fractional order derivatives that is missing from the integer-order counterparts. Several phenomena have adopted non-integer order derivatives and integrals to capture intrinsic and hidden properties of the models involved. These applications are found in biological modeling (infectious disease modeling), viscoelasticity, control theory of dynamical systems, anomalous transport and anomalous diffusion, nanotechnology, financial modeling, and random walk.

The Special Issue aims to establish a collection of scholarly articles dealing with the new trends in fractional calculus with varieties of applications in engineering and biology (especially infectious disease modeling). Rigorous analysis and theories, computational modeling, and numerical analysis articles on the topic are welcome.

Dr. Olaniyi S Iyiola
Prof. Erkan Nane
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fractional Calculus
  • Fractional Differential Equations
  • Infectious Disease Modeling
  • Existence and Uniqueness
  • Analytical and Numerical Methods

Published Papers (5 papers)

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Research

15 pages, 328 KiB  
Article
Separate Fractional (p,q)-Integrodifference Equations via Nonlocal Fractional (p,q)-Integral Boundary Conditions
by Thongchai Dumrongpokaphan, Sotiris K. Ntouyas and Thanin Sitthiwirattham
Symmetry 2021, 13(11), 2212; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13112212 - 19 Nov 2021
Cited by 2 | Viewed by 1029
Abstract
In this paper, we study a boundary value problem involving (p,q)-integrodifference equations, supplemented with nonlocal fractional (p,q)-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a [...] Read more.
In this paper, we study a boundary value problem involving (p,q)-integrodifference equations, supplemented with nonlocal fractional (p,q)-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a fixed-point problem, by considering a linear variant of the problem at hand. Once the fixed-point operator is available, existence and uniqueness results are established using the classical Banach’s and Schaefer’s fixed-point theorems. The application of the main results is demonstrated by presenting numerical examples. Moreover, we study some properties of (p,q)-integral that are used in our study. Full article
(This article belongs to the Special Issue New Trends in Fractional Calculus and Applications in Engineering and Infectious Diseases)
11 pages, 294 KiB  
Article
Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives
by Bilal Basti, Nacereddine Hammami, Imadeddine Berrabah, Farid Nouioua, Rabah Djemiat and Noureddine Benhamidouche
Symmetry 2021, 13(8), 1431; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13081431 - 04 Aug 2021
Cited by 14 | Viewed by 2115
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue New Trends in Fractional Calculus and Applications in Engineering and Infectious Diseases)
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13 pages, 851 KiB  
Article
Newton’s Law of Cooling with Generalized Conformable Derivatives
by Miguel Vivas-Cortez, Alberto Fleitas, Paulo M. Guzmán, Juan E. Nápoles and Juan J. Rosales
Symmetry 2021, 13(6), 1093; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13061093 - 21 Jun 2021
Cited by 9 | Viewed by 2815
Abstract
In this communication, using a generalized conformable differential operator, a simulation of the well-known Newton’s law of cooling is made. In particular, we use the conformable t1−α, e(1−α)t and non-conformable t−α [...] Read more.
In this communication, using a generalized conformable differential operator, a simulation of the well-known Newton’s law of cooling is made. In particular, we use the conformable t1−α, e(1−α)t and non-conformable t−α kernels. The analytical solution for each kernel is given in terms of the conformable order derivative 0<α≤1. Then, the method for inverse problem solving, using Bayesian estimation with real temperature data to calculate the parameters of interest, is applied. It is shown that these conformable approaches have an advantage with respect to ordinary derivatives. Full article
(This article belongs to the Special Issue New Trends in Fractional Calculus and Applications in Engineering and Infectious Diseases)
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26 pages, 29312 KiB  
Article
System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions
by Olaniyi Iyiola, Bismark Oduro, Trevor Zabilowicz, Bose Iyiola and Daniel Kenes
Symmetry 2021, 13(5), 787; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13050787 - 02 May 2021
Cited by 15 | Viewed by 2468
Abstract
The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with [...] Read more.
The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries. Full article
(This article belongs to the Special Issue New Trends in Fractional Calculus and Applications in Engineering and Infectious Diseases)
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21 pages, 22073 KiB  
Article
Efficacious Analytical Technique Applied to Fractional Fornberg–Whitham Model and Two-Dimensional Fractional Population Model
by Cyril D. Enyi
Symmetry 2020, 12(12), 1976; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12121976 - 30 Nov 2020
Cited by 2 | Viewed by 1470
Abstract
This paper presents an efficacious analytical and numerical method for solution of fractional differential equations. This technique, here in named q-HATM (q-homotopy analysis transform method) is applied to a one-dimensional fractional Fornberg–Whitham model and a two-dimensional fractional population model emanating [...] Read more.
This paper presents an efficacious analytical and numerical method for solution of fractional differential equations. This technique, here in named q-HATM (q-homotopy analysis transform method) is applied to a one-dimensional fractional Fornberg–Whitham model and a two-dimensional fractional population model emanating from biological sciences. The overwhelming agreement of our analytical solution by the q-HATM technique with the exact solution indeed establishes the efficacy of q-HATM to solve the fractional Fornberg–Whitham model and the two-dimensional fractional population model. Furthermore, comparisons by means of extensive analysis using numerics, graphs and error analysis are presented to affirm the preference of q-HATM technique over other methods. A variant of the q-HATM using symmetry can also be considered to solve these problems. Full article
(This article belongs to the Special Issue New Trends in Fractional Calculus and Applications in Engineering and Infectious Diseases)
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