Article
Mathematics, Interdisciplinary Applications
Javed Khan, Mati Ur Rahman, Muhammad Bilal Riaz, Jan Awrejcewicz
Summary: This paper studies the dynamics of the Dengue disease model using a novel piecewise derivative approach. The existence and uniqueness of a solution with piecewise derivative are examined, and a numerical simulation is conducted. The work clarifies the concept of piecewise derivatives and the dynamics of the crossover problem.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Multidisciplinary Sciences
Muhammad Arif, Poom Kumam, Wiyada Kumam, Ali Akgul, Thana Sutthibutpong
Summary: The study investigates the application of fractal-fractional derivatives in the model of couple stress fluid, showing the more general nature of fractal-fractional solutions compared to classical and fractional solutions. Additionally, the fractal-fractional model exhibits better memory effect on the dynamics of couple stress fluid in channel compared to the fractional model of CSF.
SCIENTIFIC REPORTS
(2021)
Article
Mechanics
Huilin Deng, Hongwei Zhou, Qing Wei, Lifeng Li, Wenhao Jia
Summary: This paper proposes a new AB fractional-order dashpot and conducts a comparative study. The results show that the new dashpot can capture the memory effect of the traditional Riemann-Liouville fractional-order dashpot and can describe the viscoelastic behavior of materials as a function of time. By introducing the AB fractional-order dashpot into the model, a new creep model is established and analytically solved using the Laplace transform. The fitting results of the experimental data show that the new creep model has a better fitting capability than the traditional models.
MECHANICS OF TIME-DEPENDENT MATERIALS
(2022)
Article
Physics, Multidisciplinary
Lalchand Verma, Ramakanta Meher
Summary: This study develops a novel fuzzy fractional model for the human liver and utilizes ABC gH-differentiability and a fuzzy double parametric q-homotopy analysis method. Numerical experiments show that the proposed method is more accurate and superior to the generalized Mittag-Leffler function method, as it coincides with most clinical data.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Applied
Ahu Ercan
Summary: This article presents the application of the Laplace-Adomian decomposition method (LADM) in dealing with nonlinear fractional Sturm-Liouville problems. By defining different types of fractional derivatives and using this method, approximate solutions are obtained, and new solutions to fractional-order SL equations are derived. Fractional calculus provides more data and is widely used in mathematical modeling.
Article
Mathematics, Interdisciplinary Applications
Kishor D. Kucche, Sagar T. Sutar
Summary: In this paper, estimations on the Atangana-Baleanu-Caputo fractional derivative at extreme points are determined, leading to comparison results. Peano's type existence results for nonlinear fractional differential equations involving Atangana-BaleanuCaputo fractional derivative are established. The acquired comparison results are then used to address the existence of local, extremal, and global solutions.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Mubashara Wali, Sadia Arshad, Sayed M. Eldin, Imran Siddique
Summary: In this study, the approximate solutions for time-space fractional linear and nonlinear diffusion equations are obtained. A finite difference approach is used to solve both linear and nonlinear fractional order diffusion problems. The Riesz fractional derivative in space is approximated using a centered difference scheme. The stability and convergence of the proposed scheme are analyzed, and the results show that the recommended method converges at a rate of O(delta t2 + h2) for mesh size h and time steps delta t. The application of the model is also examined through graphic results and numerical examples.
Article
Materials Science, Multidisciplinary
Mohammad Partohaghighi, Marzieh Mortezaee, Ali Akgul, Sayed M. Eldin
Summary: Transport of contaminants is a crucial environmental issue, and accurate modeling is vital for effective management strategies. This study introduces a non-integer model for the advection-dispersion problem in contaminant transport. The numerical solution is obtained using discrete Chebyshev polynomials and an operational matrix. The suggested scheme is validated through comparison with other numerical methods.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Ivan Area, Juan J. Nieto
Summary: In this paper, the Prabhakar fractional logistic differential equation is considered and other logistic differential equations are recovered using appropriate limit relations, with solutions represented in terms of a formal power series. Numerical approximations are implemented using truncated series.
FRACTAL AND FRACTIONAL
(2021)
Article
Engineering, Multidisciplinary
Noufe H. Aljahdaly, Rasool Shah, Ravi P. Agarwal, Thongchai Botmart
Summary: This study investigates the fractional system of the third-order Korteweg-De Vries equation using the Homotopy perturbation transform method. The results of the non-linear model are obtained by applying the Caputo, Atangana-Baleanu, and Yang-Srivastava-Machado operators. The research demonstrates that the proposed method is reliable, efficient, and applicable to various physical systems.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Materials Science, Multidisciplinary
Badr Saad T. Alkahtani, Ilknur Koca
Summary: In this paper, the applicability of fractional stochastic differential equations in an SIR model was further explored. The analysis and numerical simulations were conducted for different fractional orders and densities of randomness, providing insights into the processes following both randomness and memory nonlocality.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Omar Abu Arqub, Jagdev Singh, Mohammed Alhodaly
Summary: This study presents a mathematical modeling approach for uncertain fractional integrodifferentials (FIDEs) in electric circuits, signal processing, electromagnetics, and anomalous diffusion systems. A numerical method based on the reproducing kernel algorithm (RKA) is used to solve groups of fuzzy fractional integrodifferentials (FFIDEs) with Atangana-Baleanu-Caputo (ABC) fractional distributed order derivatives. Experimental results demonstrate the feasibility and accuracy of the proposed approach, indicating its potential for treating various models with fractional ABC distributed order.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Iskander Tlili, Nehad Ali Shah, Saif Ullah, Humera Manzoor
Summary: The study analyzed a one-dimensional generalized fractional advection-diffusion equation with a time-dependent concentration source on the boundary, obtaining an analytical solution using Laplace transform and finite sine-Fourier transform. The impact of memory parameter on solute concentration was investigated, revealing that the solute concentration increases with fractional parameter. The study also found that an advection-diffusion process described by Atangana-Baleanu time-fractional derivative leads to a smaller solute concentration compared to the classical process for a constant concentration source on the boundary.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Multidisciplinary Sciences
Hasan S. Panigoro, Agus Suryanto, Wuryansari Muharini Kusumawinahyu, Isnani Darti
Summary: This paper presents a fractional-order eco-epidemic model based on the Rosenzweig-MacArthur predator-prey model, utilizing Caputo and ABC fractional differential operators to obtain solutions. Numerical simulations show similar dynamics between the two models, with the main difference being the convergence rate to stable equilibrium points.
Article
Mathematics, Applied
Ramazan Ozarslan
Summary: This article examines the use of the two-parameter Weibull model with new fractional differential operators to analyze microbial survival curves, comparing the effects of different fractional derivatives on microbial cell survival and growth rates, and discussing the advantages and disadvantages of different fractional derivatives.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Engineering, Multidisciplinary
Onur Alp Ilhan, Haci Mehmet Baskonus, M. Nurul Islam, M. Ali Akbar, Danyal Soybas
Summary: This paper discusses the significant modeling equations for biological population and ion-acoustic waves, and proposes a new method for solving these equations, which can provide closed-form solutions and analyze the internal structure of the solutions through diagrams.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Engineering, Multidisciplinary
Nauman Raza, Ahmad Javid, Asma Rashid Butt, Haci Mehmet Baskonus
Summary: This paper discusses the integrability of a variable coefficient fifth order nonlinear Schrödinger's equation that describes the dynamics of attosecond pulses in inhomogeneous fibers. The use of variable coefficients allows for the consideration of nonuniform boundaries and media inhomogeneities. The well-known exp(-phi(s)) expansion method is employed to obtain singular and periodic solitons, and their structures and existence criteria are discussed. Modulation instability analysis and dispersion relation extraction are also performed, and comprehensive discussions and graphics are provided.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Computer Science, Theory & Methods
Ravi Shanker Dubey, Pranay Goswami, Haci Mehmet Baskonus, Tailor A. Gomati
Summary: In our research work, we propose a modified minimal model of fractional order and analyze it using the homotopy decomposition method (HDM). The minimal model is a useful mathematical model that describes the behavior of glucose-insulin metabolism. The original model was introduced in the 80s and has been updated over time. In this modified model, we include a crucial factor, the diet, which plays a significant role in blood-glucose analysis. Numerical results are obtained using the HDM, which is highly useful, significant, and simple. We also discuss the existence and uniqueness of the fractional model.
INTERNATIONAL JOURNAL OF MODELING SIMULATION AND SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Electrical & Electronic
Hajar F. F. Ismael, Haci Mehmet Baskonus, Hasan Bulut, Wei Gao
Summary: In this paper, the modified exponential function method is used to obtain new analytical solutions of the nonlinear Gerdjikov-Ivanov equation with the M-fractional operator. The novel solutions are expressed in hyperbolic, trigonometric, and exponential function forms. In addition, the instability modulation and gain spectra of the Gerdjikov-Ivanov equation are analyzed. Constraints conditions are utilized to verify the existence of the solutions. The presented solutions are novel and satisfy the M-fractional Gerdjikov-Ivanov equation.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Mathematics, Applied
Jianzhang Wu, Jiabin Yuan, Haci Mehmet Baskonus, Wei Gao
Summary: The existence of factor and fractional factor in network graph in various settings has garnered significant attention. This implies the availability of data transmission and network segmentation in specific scenarios. The paper focuses on the study of P-=2-factor and P-=3-factor, which are two special cases of the general H-factor. It investigates the existence of these path factors when certain subgraphs are forbidden and provides conclusions regarding network parameters such as factor-deleted graph, factor critical-covered graph, and factor uniform graph. The paper also demonstrates that these bounds are optimal in some sense.
JOURNAL OF FUNCTION SPACES
(2023)
Article
Materials Science, Multidisciplinary
Arkaprovo Chakraborty, P. Veeresha, Armando Ciancio, Haci Mehmet Baskonus, Mansoor Alsulami
Summary: This paper modifies the surface energy balance-mass balance model of the Cryosphere by incorporating the radiative forcing of CO2 and explores the changes in nature caused by global warming. The modified model shows chaotic behavior for certain values of CO2 radiative forcing. The research highlights the importance of the interaction between climate dynamics and complex system behavior, providing insights into the transition from stability to chaos in the Cryosphere model due to CO2 radiative forcing.
RESULTS IN PHYSICS
(2023)
Article
Mathematics
Adnan Ahmad Mahmud, Tanfer Tanriverdi, Kalsum Abdulrahman Muhamad, Haci Mehmet Baskonus
Summary: In this research, the generalized Korteweg-de Varies-Zakharov-Kuznetsov equation (gKdV-ZK) in (3+1)-dimension was investigated to study the influence of a magnetic field on weak ion-acoustic waves in plasma physics. By utilizing modified extended tanh and extended rational sinh-cosh methods, a wide range of wave structures were analyzed and hyperbolic, periodic, and traveling wave solutions were obtained along with solitary wave solutions. The solutions presented here were found to be distinctive compared to well-known outcomes. Additionally, the results were visualized in 3-dimensional, 2-dimensional, and contour profile graphs to illustrate the dynamics based on parameter selection. The suggested computational techniques were concluded to be simple, dynamic, and well-organized, making them useful for numerical calculations of complex nonlinear problems.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS
(2023)
Article
Engineering, Biomedical
Firat Evirgen, Fatma Ozkose, Mehmet Yavuz, Necati Ozdemir
Summary: This paper presents a study on the relationship between heart attacks and the Omicron variant, using a novel mathematical model. The model uses two adjustable parameters to control the number of infected individuals and individuals with the Omicron variant. The study evaluates the model's positivity and boundedness, assesses the reproduction number (R0), and conducts a sensitivity analysis of the control parameters based on the reproduction number. The model's parameters are estimated using the widely used least squares curve fitting method, using real COVID-19 cases from Tu & BULL; rkiye. Finally, numerical simulations demonstrate the effectiveness of the suggested controls in reducing the number of infected individuals and the Omicron population.
AIMS BIOENGINEERING
(2023)
Article
Engineering, Biomedical
Mehmet Yavuz, Waled Yaviz Ahmed Haydar
Summary: Mathematical modelling has been widely used and proved its significance in infectious disease control, including COVID-19. This study presents a mathematical model for COVID-19 disease, considering various populations and their interactions. The stability analysis, estimation of model parameters using real data, and numerical simulations provide insights into the future course of the disease.
AIMS BIOENGINEERING
(2023)
Article
Mathematics, Applied
Mehmet Yavuz, Fatma Ozkose, Muzeyyen Akman, Zehra Tugba Tastan
Summary: Compared to other infectious diseases, tuberculosis has a high mortality rate. A mathematical model is created in this research, considering the underlying assumptions of the disease. The main innovations of the study include two different treatment strategies and the inclusion of susceptible, latent, infected, and recovered populations in the six-dimensional model. Numerical simulations and graphic analysis are used to obtain the results.
MATHEMATICAL MODELLING AND CONTROL
(2023)
Article
Biophysics
Yasir Nadeem Anjam, Mehmet Yavuz, Mati ur Rahman, Amna Batool
Summary: Water pollution is a global issue that requires constant monitoring and revision of water resource policies to protect the environment. This study examines the dynamics of three interconnected lakes using a fractional-order model and analyzes a system of linear equations representing the waterways to investigate lake pollution. Numerical solutions are obtained using the Laplace transform with the Adomian decomposition method and the Homotopy perturbation method. Various models are considered and numerical simulations are conducted using MATLAB. The results are supported by graphical illustrations and validate the suitability of the proposed model for addressing water pollution.
Article
Mathematical & Computational Biology
Bibi Fatima, Mehmet Yavuz, Mati Ur Rahman, Fuad S. Al-Duais
Summary: Since the outbreak of MERS-CoV in the Middle East in 2012, we have developed a deterministic theoretical model to understand its transmission and calculate its basic reproduction number (R0) for airborne transmission. Using stability theory, we analyze the local and global features of the model and study the sensitivity of R0 to each parameter. Our model incorporates time-dependent control variables, such as supportive care, surgical masks, government campaigns, and treatment, to minimize infections and intervention costs. Numerical simulations are presented to support our analysis.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Onur Alp Ilhan, Fatma Berna Benli, M. Nurul Islam, M. Ali Akbar, Haci Mehmet Baskonus
Summary: In this study, we use the auxiliary equation method and fractional complex transformation to extract functional and further general exact wave solutions. The method is convenient, reliable, and provides fresh and useful solutions for fractional differential equations in physical and engineering sciences.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Haci Mehmet Baskonus, Mustafa Kayan
Summary: This paper applies the powerful Bernoulli sub-equation function method to solve partial differential equations with high non-linearity, and reports several new traveling wave solutions. The wave behaviors of the obtained results, including 2D, 3D, and contour surfaces, are observed under suitable parameter values.
APPLIED MATHEMATICS AND NONLINEAR SCIENCES
(2023)
Article
Mathematics, Applied
Khalid K. Ali, Mohamed S. Osman, Haci Mehmet Baskonus, Nasser S. Elazabb, Esin Ilhan
Summary: This paper presents a numerical and analytical study on the HIV-1 infection of CD4(+) T-cells using a conformable fractional mathematical model. The model is analyzed using Kudryashov and modified Kudryashov methods, and numerically studied using the finite difference method. A comparison between the results obtained from the analytical and numerical methods is conducted, and figures are provided to demonstrate the accuracy of the solutions obtained.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Physics, Multidisciplinary
Xiaoyu Shi, Jian Zhang, Xia Jiang, Juan Chen, Wei Hao, Bo Wang
Summary: This study presents a novel framework using offline reinforcement learning to improve energy consumption in road transportation. By leveraging real-world human driving trajectories, the proposed method achieves significant improvements in energy consumption. The offline learning approach demonstrates generalizability across different scenarios.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Junhyuk Woo, Soon Ho Kim, Hyeongmo Kim, Kyungreem Han
Summary: Reservoir computing (RC) is a new machine-learning framework that uses an abstract neural network model to process information from complex dynamical systems. This study investigates the neuronal and network dynamics of liquid state machines (LSMs) using numerical simulations and classification tasks. The findings suggest that the computational performance of LSMs is closely related to the dynamic range, with a larger dynamic range resulting in higher performance.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Yuwei Yang, Zhuoxuan Li, Jun Chen, Zhiyuan Liu, Jinde Cao
Summary: This paper proposes an extreme learning machine (ELM) algorithm based on residual correction and Tent chaos sequence (TRELM-DROP) for accurate prediction of traffic flow. The algorithm reduces the impact of randomness in traffic flow through the Tent chaos strategy and residual correction method, and avoids weight optimization using the iterative method. A DROP strategy is introduced to improve the algorithm's ability to predict traffic flow under varying conditions.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Chengwei Dong, Min Yang, Lian Jia, Zirun Li
Summary: This work presents a novel three-dimensional system with multiple types of coexisting attractors, and investigates its dynamics using various methods. The mechanism of chaos emergence is explored, and the periodic orbits in the system are studied using the variational method. A symbolic coding method is successfully established to classify the short cycles. The flexibility and validity of the system are demonstrated through analogous circuit implementation. Various chaos-based applications are also presented to show the system's feasibility.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Viorel Badescu
Summary: This article discusses the maximum work extraction from confined particles energy, considering both reversible and irreversible processes. The results vary for different types of particles and conditions. The concept of exergy cannot be defined for particles that undergo spontaneous creation and annihilation. It is also noted that the Carnot efficiency is not applicable to the conversion of confined thermal radiation into work.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
P. M. Centres, D. J. Perez-Morelo, R. Guzman, L. Reinaudi, M. C. Gimenez
Summary: In this study, a phenomenological investigation of epidemic spread was conducted using a model of agent diffusion over a square region based on the SIR model. Two possible contagion mechanisms were considered, and it was observed that the number of secondary infections produced by an individual during its infectious period depended on various factors.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Zuan Jin, Minghui Ma, Shidong Liang, Hongguang Yao
Summary: This study proposes a differential variable speed limit (DVSL) control strategy considering lane assignment, which sets dynamic speed limits for each lane to attract vehicle lane-changing behaviors before the bottleneck and reduce the impact of traffic capacity drop. Experimental results show that the proposed DVSL control strategy can alleviate traffic congestion and improve efficiency.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Matthew Dicks, Andrew Paskaramoorthy, Tim Gebbie
Summary: In this study, we investigate the learning dynamics of a single reinforcement learning optimal execution trading agent when it interacts with an event-driven agent-based financial market model. The results show that the agents with smaller state spaces converge faster and are able to intuitively learn to trade using spread and volume states. The introduction of the learning agent has a robust impact on the moments of the model, except for the Hurst exponent, which decreases, and it can increase the micro-price volatility as trading volumes increase.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Zhouzhou Yao, Xianyu Wu, Yang Yang, Ning Li
Summary: This paper developed a cooperative lane-changing decision system based on digital technology and indirect reciprocity. By introducing image scoring and a Q-learning based reinforcement learning algorithm, drivers can continuously evaluate gains and adjust their strategies. The study shows that this decision system can improve driver cooperation and traffic efficiency, achieving over 50% cooperation probability under any connected vehicles penetration and traffic density, and reaching 100% cooperation probability under high penetration and medium to high traffic density.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Josephine Nanyondo, Henry Kasumba
Summary: This paper presents a multi-class Aw-Rascle (AR) model with area occupancy expressed in terms of vehicle class proportions. The qualitative properties of the proposed equilibrium velocity and the stability conditions of the model are established. The numerical results show the effect of proportional densities on the flow of vehicle classes, indicating the realism of the proposed model.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Oliver Smirnov
Summary: This study proposes a new method for simultaneously estimating the parameters of the 2D Ising model. The method solves a constrained optimization problem, where the objective function is a pseudo-log-likelihood and the constraint is the Hamiltonian of the external field. Monte Carlo simulations were conducted using models of different shapes and sizes to evaluate the performance of the method with and without the Hamiltonian constraint. The results demonstrate that the proposed estimation method yields lower variance across all model shapes and sizes compared to a simple pseudo-maximum likelihood.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Przemyslaw Chelminiak
Summary: The study investigates the first-passage properties of a non-linear diffusion equation with diffusivity dependent on the concentration/probability density through a power-law relationship. The survival probability and first-passage time distribution are determined based on the power-law exponent, and both exact and approximate expressions are derived, along with their asymptotic representations. The results pertain to diffusing particles that are either freely or harmonically trapped. The mean first-passage time is finite for the harmonically trapped particle, while it is divergent for the freely diffusing particle.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Hidemaro Suwa
Summary: The choice of transition kernel is crucial for the performance of the Markov chain Monte Carlo method. A one-parameter rejection control transition kernel is proposed, and it is shown that the rejection process plays a significant role in determining the sampling efficiency.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Xudong Wang, Yao Chen
Summary: This article investigates the joint influence of expanding medium and constant force on particle diffusion. By starting from the Langevin picture and introducing the effect of external force in two different ways, two models with different force terms are obtained. Detailed analysis and derivation yield the Fokker-Planck equations and moments for the two models. The sustained force behaves as a decoupled force, while the intermittent force changes the diffusion behavior with specific effects depending on the expanding rate of the medium.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
