Article
Mathematics, Applied
Juan J. Nieto
Summary: We studied the logistic differential equation of fractional order and non-singular kernel, and obtained the analytical solution.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Juan J. Nieto
Summary: We solve the logistic differential equation for generalized proportional Caputo fractional derivative using a fractional power series solution. The coefficients of the power series are connected to Euler polynomials, Euler numbers, and a recently introduced sequence of Euler's fractional numbers. Numerical approximations are provided to demonstrate the accuracy of truncating the fractional power series. This extends previous studies on the Caputo fractional logistic differential equation and Euler numbers.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2022)
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
Mathematics, Interdisciplinary Applications
Jun-Sheng Duan, Ming Li, Yan Wang, Yu-Lian An
Summary: This article considers the approximate solutions using quadratic splines for a fractional differential equation with two Caputo fractional derivatives. Numerical computing schemes for the derivatives are derived based on quadratic spline interpolation function, and the recursion scheme and approximate solution are generated. The proposed method is validated through numerical examples and compared with L1-L2 numerical solutions.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Chun Yun Kee, Cherq Chua, Muhammad Zubair, L. K. Ang
Summary: This study improves the urban growth model by considering memory effects and proposes a new model based on fractional calculus. By testing the new model on different urban attributes, it is found that the fractional model provides better agreement with annual population growth and can estimate useful parameters for urban planning and decision-making.
Article
Mathematics, Interdisciplinary Applications
Najla M. Alarifi, Rabha W. Ibrahim
Summary: Special functions, typically named after early scientists, have specific applications in mathematical physics or other areas of mathematics. By using q-fractional calculus, the geometric properties of the generalized Prabhakar fractional differential operator in the open unit disk are investigated. The methodology involves the use of differential subordination and superordination theory, resulting in the organization of numerous fractional differential inequalities and the study of solutions to special kinds of q-fractional differential equations.
FRACTAL AND FRACTIONAL
(2022)
Article
Materials Science, Multidisciplinary
Jyoti Mishra
Summary: This paper investigates a system of partial differential equations that describes the behavior of the telegraph. By converting the time differential operators to nonlocal operators, nonlocal behaviors are incorporated into the mathematical formulation. Numerical solutions are presented using Newton's polynomial interpolation, and exact solutions are attempted to be derived through Laplace transform.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
Shahid Ahmed, Shah Jahan, Kottakkaran S. Nisar
Summary: The aim of this study is to develop the Fibonacci wavelet method together with the quasi-linearization technique to solve the fractional-order logistic growth model. The block-pulse functions are employed to construct the operational matrices of fractional-order integration. The present time-fractional population growth model is converted into a set of nonlinear algebraic equations using the proposed generated matrices. Numerical simulations are conducted to show the reliability and use of the suggested approach when contrasted with methods from the existing literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Ahmed F. Abdel Jalil, Ayad R. Khudair
Summary: In this paper, we successfully solve some linear fractional differential equations (FDE) analytically by transforming them into linear differential equations with integer orders. By solving an auxiliary linear differential equation, certain terms of the original FDE are eliminated, resulting in the remaining terms being a solution to the auxiliary equation. Several examples are provided to demonstrate the ability and efficacy of this method.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Engineering, Mechanical
Nazek A. Obeidat, Daniel E. Bentil
Summary: This paper develops a new technique called the Tempered Fractional Natural Transform Method for solving problems in tempered fractional linear and nonlinear ordinary and partial differential equations. The method's theorems, properties, and exact solutions to well-known problems are rigorously proven, making it a viable alternative in the field with wide applications in science and engineering.
NONLINEAR DYNAMICS
(2021)
Article
Multidisciplinary Sciences
Diego Caratelli, Pierpaolo Natalini, Paolo Emilio Ricci
Summary: In this paper, we utilize power series with rational exponents to obtain exact solutions for initial value problems of fractional differential equations. By constructing recursions for expansion coefficients, certain problems previously studied in the literature can be solved analytically and approximate solutions can be derived.
Article
Mathematics, Interdisciplinary Applications
Jun-Sheng Duan, Li-Xia Jing, Ming Li
Summary: This study focuses on the boundary value problem (BVP) for the varying coefficient linear Caputo-type fractional differential equation subject to mixed boundary conditions on the interval 0 <= x <= 1. The BVP is transformed into an equivalent differential-integral equation by merging the boundary conditions. The shifted Chebyshev polynomials and the collocation method are employed to solve the differential-integral equation. The varying coefficients are decomposed into truncated shifted Chebyshev series, allowing accurate calculations of integrals. Numerical examples are provided to verify the effectiveness of the proposed method.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Dumitru Baleanu, Rabha W. Ibrahim
Summary: In this paper, we propose a mathematical model to describe impulsive behavior using integro-differential equations (I-DE). We investigate the periodic boundary value problems for a class of fractional I-DEs with non-quick impulses in Banach spaces. Utilizing the measure of non-compactness, the method of resolving domestic, and the fixed point result, we provide several sufficient conditions for the existence of mild outcomes for I-DE. Finally, we present a set of examples to illustrate the key findings of our research, which are contributed to recent works in this field.
Article
Mathematics, Applied
Samy A. Harisa, Chokkalingam Ravichandran, Kottakkaran Sooppy Nisar, Nashat Faried, Ahmed Morsy
Summary: In this paper, the behavior of the neutral integro-differential equations of fractional order including the Caputo-Hadamard fractional derivative is analyzed using the topological degree method. The suggested fixed point technique is validated by specific numerical examples, demonstrating its wide applicability and high efficiency.
Article
Mathematics, Applied
Sunil Dutt Purohit, Dumitru Baleanu, Kamlesh Jangid
Summary: In this article, solutions of a generalised multiorder fractional partial differential equations involving the Caputo time-fractional derivative and the Riemann-Liouville space fractional derivatives are studied using the Laplace-Fourier transform technique. The proposed equations can be reduced to the Schrodinger equation, wave equation, and diffusion equation in a more general sense. Solutions of the equation proposed in the stochastic resetting theory in the context of Brownian motion are also found in a general regime.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Engineering, Multidisciplinary
Ivan Area, Xurxo Hervada Vidal, Juan J. Nieto, Maria Jesus Purrinos Hermida
Summary: This study presents a method to estimate the number of required beds at intensive care units in advance using a mathematical compartmental model that includes the super-spreader class. Numerical simulations were conducted to demonstrate the accuracy of the predictions compared to real data in Galicia.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Faical Ndairou, Ivan Area, Juan J. Nieto, Cristiana J. Silva, Delfim F. M. Torres
Summary: A novel fractional compartmental mathematical model was proposed to study the spread of COVID-19, with a focus on the transmissibility of super-spreaders. Numerical simulations were conducted for the regions of Galicia, Spain, and Portugal, revealing different values of the Caputo derivative order and highlighting the importance of considering fractional models.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Multidisciplinary Sciences
Cristiana J. Silva, Carla Cruz, Delfim F. M. Torres, Alberto P. Munuzuri, Alejandro Carballosa, Ivan Area, Juan J. Nieto, Rui Fonseca-Pinto, Rui Passadouro, Estevao Soares dos Santos, Wilson Abreu, Jorge Mira
Summary: The COVID-19 pandemic has forced policy makers to implement urgent lockdowns, and now societies need to balance the need to reduce infection rates with reopening the economy. Mathematical models and data analysis can be used to predict the consequences of political decisions.
SCIENTIFIC REPORTS
(2021)
Article
Environmental Sciences
Ivan Area, Henrique Lorenzo, Pedro J. Marcos, Juan J. Nieto
Summary: This study analyzed four key variables in Galicia (NW Spain) after one year of the COVID-19 pandemic, focusing on different age groups and their representation in society, providing insights for the scheduling of vaccination process and exploring the reasons for different impacts of the pandemic in different regions.
INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH
(2021)
Article
Mathematics
Yves Guemo Tefo, Rabia Aktas, Ivan Area, Esra Guldogan Lekesiz
Summary: A new class of partial differential equations with symmetric orthogonal solutions is introduced in this study, where orthogonality is obtained using the Sturm-Liouville approach. The general case is analyzed in detail, providing orthogonality weight function, three-term recurrence relations for monic orthogonal polynomial solutions, and explicit form of these solutions.
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Ivan Area, Francisco J. Fernandez, Juan J. Nieto, F. Adrian F. Tojo
Summary: This paper introduces the concept of a digital twin using Stieltjes differential equations and presents a precise mathematical definition of the solution to the problem. The existence and uniqueness of solutions are also analyzed and the concept of the main digital twin is introduced. Using the classical SIR epidemic model as an example, the interrelation between the digital twin and the system is studied, and Stieltjes derivatives are used to feed real system data to the virtual model, improving it in real time. Numerical simulations with real COVID-19 epidemic data demonstrate the accuracy of the proposed ideas.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
I Area, Y. Guemo Tefo
Summary: This paper explicitly provides monic families of bivariate Askey-Wilson polynomials and q-Racah polynomials. Monic families of bivariate orthogonal polynomials in both quadratic and q-quadratic lattices are also explicitly given using appropriate limit relations.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics
Esra Guldogan Lekesiz, Rabia Aktas, Ivan Area
Summary: This paper presents the Fourier transform of multivariate orthogonal polynomials on the simplex. A new family of multivariate orthogonal functions is obtained using the Parseval's identity, and several recurrence relations are derived.
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics
Pablo Boullosa, Adrian Garea, Ivan Area, Juan J. Nieto, Jorge Mira
Summary: This paper proposes an empirical dynamic modeling method to predict the evolution of influenza in different regions and extends it to predict other epidemics. The researchers also investigate the geographical distribution of influenza and COVID-19 through network analysis.
Article
Mathematics, Applied
Rabia Aktas, Ivan Area, Teresa E. Perez
Summary: This paper studies the three term relations of orthogonal polynomials in several variables associated with a moment linear functional obtained by a Uvarov modification. It analyzes the existence of Uvarov orthogonal polynomials and provides conditions to ensure their existence. The matrices of the three term relations for the Uvarov orthogonal polynomials are explicitly given based on the matrices of the three term relations satisfied by the original family. Two examples are presented to demonstrate the validity of the results for positive definite linear functionals and some quasi definite linear functionals which are not positive definite.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Esra Guldogan Lekesiz, Ivan Area
Summary: This paper generalizes the study of finite sequences of orthogonal polynomials from one to two variables and presents twenty three new classes of bivariate finite orthogonal polynomials. Various properties of these polynomial classes, including weight function, domain of orthogonality, recurrence relations, partial differential equations, etc., are introduced.
Article
Mathematics, Applied
Esra Guldogan Lekesiz, Rabia Aktas, Ivan Area
Summary: This paper explores the Fourier transform of orthogonal polynomial systems and focuses on the Hermite functions and multivariate orthogonal polynomials on the unit ball. By using the Fourier transform and Parseval's identity, a new family of orthogonal functions is introduced.
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
Mathematics, Applied
Xiao-Li Ding, Ivan Area, Juan J. Nieto
Summary: This paper focuses on the optimal control problems of an epidemic system governed by a class of singular evolution equations, aiming to minimize the impact of the COVID-19 pandemic on the world. By using mathematical models, the study explores well-posedness in an appropriate functional space and presents an optimal control problem to reduce costs and minimize the total number of susceptible and infected individuals.
EVOLUTION EQUATIONS AND CONTROL THEORY
(2021)
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)
