Journal Description
Axioms
Axioms
is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published monthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT), International Fuzzy Systems Association (IFSA) and Union of Slovak Mathematicians and Physicists (JSMF) are affiliated with Axioms and their members receive discounts on the article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High visibility: indexed within SCIE (Web of Science), dblp, and other databases.
- Journal Rank: JCR - Q2 (Mathematics, Applied)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 21.8 days after submission; acceptance to publication is undertaken in 2.8 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Companion journal: Logics.
Impact Factor:
2.0 (2022);
5-Year Impact Factor:
1.9 (2022)
Latest Articles
Nonuniform Sampling in Lp-Subspaces Associated with the Multi-Dimensional Special Affine Fourier Transform
Axioms 2024, 13(5), 329; https://doi.org/10.3390/axioms13050329 - 15 May 2024
Abstract
In this paper, the sampling and reconstruction problems in function subspaces of associated with the multi-dimensional special affine Fourier transform (SAFT) are discussed. First, we give the definition of the multi-dimensional SAFT and study its properties including
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In this paper, the sampling and reconstruction problems in function subspaces of associated with the multi-dimensional special affine Fourier transform (SAFT) are discussed. First, we give the definition of the multi-dimensional SAFT and study its properties including the Parseval’s relation, the canonical convolution theorems and the chirp-modulation periodicity. Then, a kind of function spaces are defined by the canonical convolution in the multi-dimensional SAFT domain, the existence and the properties of the dual basis functions are demonstrated, and the -stability of the basis functions is established. Finally, based on the nonuniform samples taken on a dense set, we propose an iterative reconstruction algorithm with exponential convergence to recover the signals in a -subspace associated with the multi-dimensional SAFT, and the validity of the algorithm is demonstrated via simulations.
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(This article belongs to the Special Issue Advances in Mathematical Methods in Signal Processing and Its Applications)
Open AccessArticle
Coercive and Noncoercive Mixed Generalized Complementarity Problems
by
Ram N. Mohapatra, Bijaya K. Sahu and Gayatri Pany
Axioms 2024, 13(5), 328; https://doi.org/10.3390/axioms13050328 - 15 May 2024
Abstract
Impressed with the very recent developments of noncoercive complementarity problems and the use of recession sets in complementarity problems, here, we discuss mixed generalized complementarity problems in Hausdorff topological vector spaces. We used the Tikhonov regularization procedure, as well as arguments from the
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Impressed with the very recent developments of noncoercive complementarity problems and the use of recession sets in complementarity problems, here, we discuss mixed generalized complementarity problems in Hausdorff topological vector spaces. We used the Tikhonov regularization procedure, as well as arguments from the recession analysis, to establish the existence of solutions for mixed generalized complementarity problems without coercivity assumptions in Banach spaces.
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(This article belongs to the Special Issue Large-Scale Optimization and Variational Inequalities: Theory and Applications)
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Mathematical Methods in Applied Sciences
by
Nuno R. O. Bastos and Touria Karite
Axioms 2024, 13(5), 327; https://doi.org/10.3390/axioms13050327 - 15 May 2024
Abstract
In this editorial, we introduce “Mathematical Methods in Applied Sciences”, a Special Issue of Axioms comprising 17 articles [...]
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(This article belongs to the Special Issue Mathematical Methods in the Applied Sciences)
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Tractability of Multivariate Approximation Problem on Euler and Wiener Integrated Processes
by
Jie Zhang
Axioms 2024, 13(5), 326; https://doi.org/10.3390/axioms13050326 - 15 May 2024
Abstract
This paper examines the tractability of multivariate approximation problems under the normalized error criterion for a zero-mean Gaussian measure in an average-case setting. The Gaussian measure is associated with a covariance kernel, which is represented by the tensor product of one-dimensional kernels corresponding
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This paper examines the tractability of multivariate approximation problems under the normalized error criterion for a zero-mean Gaussian measure in an average-case setting. The Gaussian measure is associated with a covariance kernel, which is represented by the tensor product of one-dimensional kernels corresponding to Euler and Wiener integrated processes with non-negative and nondecreasing smoothness parameters . We give matching sufficient and necessary conditions for various concepts of tractability in terms of the asymptotic properties of the regularity parameters, except for (s, 0)-WT.
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(This article belongs to the Special Issue Numerical Computation, Approximation of Functions and Applied Mathematics II)
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Multiplicity of Solutions for the Noncooperative Kirchhoff-Type Variable Exponent Elliptic System with Nonlinear Boundary Conditions
by
Yiying Mao and Yang Yang
Axioms 2024, 13(5), 325; https://doi.org/10.3390/axioms13050325 - 14 May 2024
Abstract
Considering the solutions of a class of noncooperative Kirchhoff-type -Laplacian elliptic systems with nonlinear boundary conditions, we derive a sequence of solutions utilizing both the variational method and limit index theory under certain underlying assumptions. The novelty of this
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Considering the solutions of a class of noncooperative Kirchhoff-type -Laplacian elliptic systems with nonlinear boundary conditions, we derive a sequence of solutions utilizing both the variational method and limit index theory under certain underlying assumptions. The novelty of this study is that we verify the condition using another method, diverging from the approaches cited in the previous literature.
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(This article belongs to the Special Issue Differential Equations and Related Topics)
Open AccessArticle
A Vector Representation of Multicomplex Numbers and Its Application to Radio Frequency Signals
by
Daniele Borio
Axioms 2024, 13(5), 324; https://doi.org/10.3390/axioms13050324 - 14 May 2024
Abstract
Hypercomplex numbers, which are multi-dimensional extensions of complex numbers, have been proven beneficial in the development of advanced signal processing algorithms, including multi-dimensional filter design, linear regression and classification. We focus on multicomplex numbers, sets of hypercomplex numbers with commutative products, and introduce
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Hypercomplex numbers, which are multi-dimensional extensions of complex numbers, have been proven beneficial in the development of advanced signal processing algorithms, including multi-dimensional filter design, linear regression and classification. We focus on multicomplex numbers, sets of hypercomplex numbers with commutative products, and introduce a vector representation allowing one to isolate the hyperbolic real and imaginary parts of a multicomplex number. The orthogonal decomposition of a multicomplex number is also discussed, and its connection with Hadamard matrices is highlighted. Finally, a multicomplex polar representation is provided. These properties are used to extend the standard complex baseband signal representation to the multi-dimensional case. It is shown that a set of Radio Frequency (RF) signals can be represented as the real part of a single multicomplex signal modulated by several frequencies. The signal RFs are related through a Hadamard matrix to the modulating frequencies adopted in the multicomplex baseband representation. Moreover, an orthogonal decomposition is provided for the obtained multicomplex baseband signal as a function of the complex baseband representations of the input RF signals.
Full article
(This article belongs to the Special Issue Advances in Mathematical Methods in Signal Processing and Its Applications)
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Quantum Vision Transformers for Quark–Gluon Classification
by
Marçal Comajoan Cara, Gopal Ramesh Dahale, Zhongtian Dong, Roy T. Forestano, Sergei Gleyzer, Daniel Justice, Kyoungchul Kong, Tom Magorsch, Konstantin T. Matchev, Katia Matcheva and Eyup B. Unlu
Axioms 2024, 13(5), 323; https://doi.org/10.3390/axioms13050323 - 13 May 2024
Abstract
We introduce a hybrid quantum-classical vision transformer architecture, notable for its integration of variational quantum circuits within both the attention mechanism and the multi-layer perceptrons. The research addresses the critical challenge of computational efficiency and resource constraints in analyzing data from the upcoming
[...] Read more.
We introduce a hybrid quantum-classical vision transformer architecture, notable for its integration of variational quantum circuits within both the attention mechanism and the multi-layer perceptrons. The research addresses the critical challenge of computational efficiency and resource constraints in analyzing data from the upcoming High Luminosity Large Hadron Collider, presenting the architecture as a potential solution. In particular, we evaluate our method by applying the model to multi-detector jet images from CMS Open Data. The goal is to distinguish quark-initiated from gluon-initiated jets. We successfully train the quantum model and evaluate it via numerical simulations. Using this approach, we achieve classification performance almost on par with the one obtained with the completely classical architecture, considering a similar number of parameters.
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(This article belongs to the Section Mathematical Analysis)
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A C0 Nonconforming Virtual Element Method for the Kirchhoff Plate Obstacle Problem
by
Bangmin Wu and Jiali Qiu
Axioms 2024, 13(5), 322; https://doi.org/10.3390/axioms13050322 - 13 May 2024
Abstract
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This paper investigates a novel nonconforming virtual element method (VEM) for solving the Kirchhoff plate obstacle problem, which is described by a fourth-order variational inequality (VI) of the first kind. In our study, we distinguish our approach by introducing new internal
[...] Read more.
This paper investigates a novel nonconforming virtual element method (VEM) for solving the Kirchhoff plate obstacle problem, which is described by a fourth-order variational inequality (VI) of the first kind. In our study, we distinguish our approach by introducing new internal degrees of freedom to the traditional lowest-order nonconforming VEM, which originally lacked such degrees. This addition not only facilitates error estimation but also enhances its intuitiveness. Importantly, our novel nonconforming VEM naturally satisfies the constraints of the obstacle problem. We then establish an a priori error estimate for our novel nonconforming VEM, with the result indicating that the lowest order of our method achieves optimal convergence. Finally, we present a numerical example to validate the theoretical result.
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Quasi-Configurations Derived by Special Arrangements of Lines
by
Stefano Innamorati
Axioms 2024, 13(5), 321; https://doi.org/10.3390/axioms13050321 - 11 May 2024
Abstract
A quasi-configuration is a point–line incidence structure in which each point is incident with at least three lines and each line is incident with at least three points. We investigate derived quasi-configurations that arise both by duality and intersecting lines of three special
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A quasi-configuration is a point–line incidence structure in which each point is incident with at least three lines and each line is incident with at least three points. We investigate derived quasi-configurations that arise both by duality and intersecting lines of three special arrangements of lines. Sets with few intersection numbers are provided.
Full article
(This article belongs to the Special Issue Theory of Curves and Knots with Applications)
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Stability of the Borell–Brascamp–Lieb Inequality for Multiple Power Concave Functions
by
Meng Qin, Zhuohua Zhang, Rui Luo, Mengjie Ren and Denghui Wu
Axioms 2024, 13(5), 320; https://doi.org/10.3390/axioms13050320 - 11 May 2024
Abstract
In this paper, we prove the stability of the Brunn–Minkowski inequality for multiple convex bodies in terms of the concept of relative asymmetry. Using these stability results and the relationship of the compact support of functions, we establish the stability of the Borell–Brascamp–Lieb
[...] Read more.
In this paper, we prove the stability of the Brunn–Minkowski inequality for multiple convex bodies in terms of the concept of relative asymmetry. Using these stability results and the relationship of the compact support of functions, we establish the stability of the Borell–Brascamp–Lieb inequality for multiple power concave functions via relative asymmetry.
Full article
(This article belongs to the Special Issue Advances in Convex Geometry and Analysis)
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Strategic Behavior and Optimal Inventory Level in a Make-to-Stock Queueing System with Retrial Customers
by
Yuejiao Wang and Chenguang Cai
Axioms 2024, 13(5), 319; https://doi.org/10.3390/axioms13050319 - 11 May 2024
Abstract
In this article, we consider a make-to-stock queueing system with retrial customers. Upon their arrival, customers make a decision to either join the system or not based on a reward–cost function. If customers join the retrial queue, they become repeat customers. Each repeat
[...] Read more.
In this article, we consider a make-to-stock queueing system with retrial customers. Upon their arrival, customers make a decision to either join the system or not based on a reward–cost function. If customers join the retrial queue, they become repeat customers. Each repeat customer repeats their demand after an exponential amount of time until they have been successfully served. We explore the equilibrium strategies of customers in both the almost observable and unobservable cases. Furthermore, we also analyze the expected costs of the entire system based on the customers’ behavior in these two cases. Additionally, we determine the optimal inventory levels in both cases through numerical experiments.
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(This article belongs to the Section Mathematical Analysis)
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Quasi-Contraction Maps in Subordinate Semimetric Spaces
by
Areej Alharbi, Hamed Alsulami and Maha Noorwali
Axioms 2024, 13(5), 318; https://doi.org/10.3390/axioms13050318 - 10 May 2024
Abstract
Throughout this study, we discuss the subordinate Pompeiu–Hausdorff metric (SPHM) in subordinate semimetric spaces. Moreover, we present a well-behaved quasi-contraction (WBQC) to solve quasi-contraction (QC) problems in subordinate semimetric spaces under some local constraints. Furthermore, we provide examples to support our conclusion.
Full article
(This article belongs to the Special Issue Research on Fixed Point Theory and Application)
Open AccessArticle
A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments
by
Yue-Wu Li and Feng Qi
Axioms 2024, 13(5), 317; https://doi.org/10.3390/axioms13050317 - 10 May 2024
Abstract
In this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at some specific arguments, successfully apply a special case
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In this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at some specific arguments, successfully apply a special case of the newly extended closed-form formula to derive an alternative form for the Maclaurin power series expansion of the Wilf function, and discover two novel increasing rational approximations to a quarter of the circular constant.
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Open AccessArticle
Convergence Results for History-Dependent Variational Inequalities
by
Mircea Sofonea and Domingo A. Tarzia
Axioms 2024, 13(5), 316; https://doi.org/10.3390/axioms13050316 - 10 May 2024
Abstract
We consider a history-dependent variational inequality in a real Hilbert space, for which we recall an existence and uniqueness result. We associate this inequality with a gap function, together with two additional problems: a nonlinear equation and a minimization problem. Then, we prove
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We consider a history-dependent variational inequality in a real Hilbert space, for which we recall an existence and uniqueness result. We associate this inequality with a gap function, together with two additional problems: a nonlinear equation and a minimization problem. Then, we prove that solving these problems is equivalent to solving the original history-dependent variational inequality. Next, we state and prove a convergence criterion, i.e., we provide necessary and sufficient conditions which guarantee the convergence of a sequence of functions to the solution of the considered inequality. Based on the equivalence above, we deduce various consequences that present some interest on their own, and, moreover, we obtain convergence results for the two additional problems considered. Finally, we apply our abstract results to the study of an inequality problem in solid mechanics. It concerns the study of a viscoelastic constitutive law with long memory and unilateral constraints, for which we deduce a convergence result and provide the corresponding mechanical interpretations.
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(This article belongs to the Section Hilbert’s Sixth Problem)
Open AccessArticle
Parameter Estimation in Spatial Autoregressive Models with Missing Data and Measurement Errors
by
Tengjun Li, Zhikang Zhang and Yunquan Song
Axioms 2024, 13(5), 315; https://doi.org/10.3390/axioms13050315 - 10 May 2024
Abstract
This study addresses the problem of parameter estimation in spatial autoregressive models with missing data and measurement errors in covariates. Specifically, a corrected likelihood estimation approach is employed to rectify the bias in the log-maximum likelihood function induced by measurement errors. Additionally, a
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This study addresses the problem of parameter estimation in spatial autoregressive models with missing data and measurement errors in covariates. Specifically, a corrected likelihood estimation approach is employed to rectify the bias in the log-maximum likelihood function induced by measurement errors. Additionally, a combination of inverse probability weighting (IPW) and mean imputation is utilized to mitigate the bias caused by missing data. Under several mild conditions, it is demonstrated that the proposed estimators are consistent and possess oracle properties. The efficacy of the proposed parameter estimation process is assessed through Monte Carlo simulation studies. Finally, the applicability of the proposed method is further substantiated using the Boston Housing Dataset.
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(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications)
Open AccessArticle
Some Results on Zinbiel Algebras and Rota–Baxter Operators
by
Jizhong Gao, Junna Ni and Jianhua Yu
Axioms 2024, 13(5), 314; https://doi.org/10.3390/axioms13050314 - 10 May 2024
Abstract
Rota–Baxter operators (RBOs) play a substantial role in many subfields of mathematics, especially in mathematical physics. In the article, RBOs on Zinbiel algebras (ZAs) and their sub-adjacent algebras are first investigated. Moreover, all the RBOs on two and three-dimensional ZAs are presented. Finally,
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Rota–Baxter operators (RBOs) play a substantial role in many subfields of mathematics, especially in mathematical physics. In the article, RBOs on Zinbiel algebras (ZAs) and their sub-adjacent algebras are first investigated. Moreover, all the RBOs on two and three-dimensional ZAs are presented. Finally, ZAs are also realized in low dimensions of the RBOs of commutative associative algebras. It was found that not all ZAs can be attained in this way.
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Open AccessArticle
Basic Computational Algorithms for Representing an Aircraft Flight (Calculation of 3D Displacement and Displaying)
by
Adan Ramirez-Lopez
Axioms 2024, 13(5), 313; https://doi.org/10.3390/axioms13050313 - 10 May 2024
Abstract
This manuscript describes the computational process to calculate an airplane path and display it in a 2D and 3D coordinate system on a computer screen. The airplane movement is calculated as a function of its dynamic’s conditions according to physical and logical theory.
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This manuscript describes the computational process to calculate an airplane path and display it in a 2D and 3D coordinate system on a computer screen. The airplane movement is calculated as a function of its dynamic’s conditions according to physical and logical theory. Here, the flight is divided into maneuvers and the aircraft conditions are defined as boundary conditions. Then the aircraft position is calculated using nested loops, which execute the calculation procedure at every step time (Δt). The calculation of the aircraft displacement is obtained as a function of the aircraft speed and heading angles. The simulator was created using the C++ programming language, and each part of the algorithm was compiled independently to reduce the source code, allow easy modification, and improve the programming efficiency. Aerial navigation involves very complex phenomena to be considered for an appropriate representation; moreover, in this manuscript, the influence of the mathematical approach to properly represent the aircraft flight is described in detail. The flight simulator was successfully tested by simulating some basic theoretical flights with different maneuvers, which include stationary position, running along the way, take off, and some movements in the airspace. The maximum aircraft speed tested was 120 km/h, the maximum maneuver time was 12 min, and the space for simulation was assumed to be without obstacles. Here, the geometrical description of path and speed is analyzed according to the symmetric and asymmetric results. Finally, an analysis was conducted to evaluate the approach of the numerical methods used; after that, it was possible to confirm that precision increased as the step time was reduced. According to this analysis, no more than 500 steps are required for a good approach in the calculation of the aircraft displacement.
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(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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Canonical Metrics on Twisted Quiver Bundles over a Class of Non-Compact Gauduchon Manifold
by
Shi-Fan Cai, Sudhakar Kumar Chaubey, Xin Xu, Pan Zhang and Zhi-Heng Zhang
Axioms 2024, 13(5), 312; https://doi.org/10.3390/axioms13050312 - 9 May 2024
Abstract
The aim of this paper is to prove a theorem for holomorphic twisted quiver bundles over a special non-compact Gauduchon manifold, connecting the existence of -Hermite–Yang–Mills metric in differential geometry and the analytic
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The aim of this paper is to prove a theorem for holomorphic twisted quiver bundles over a special non-compact Gauduchon manifold, connecting the existence of -Hermite–Yang–Mills metric in differential geometry and the analytic -stability in algebraic geometry. The proof of the theorem relies on the flow method and the Uhlenbeck–Yau’s continuity method.
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(This article belongs to the Special Issue Advances in Differential Geometry and Mathematical Physics)
Open AccessArticle
Study of the Six-Compartment Nonlinear COVID-19 Model with the Homotopy Perturbation Method
by
Muhammad Rafiullah, Muhammad Asif, Dure Jabeen and Mahmoud A. Ibrahim
Axioms 2024, 13(5), 311; https://doi.org/10.3390/axioms13050311 - 9 May 2024
Abstract
The current study aims to utilize the homotopy perturbation method (HPM) to solve nonlinear dynamical models, with a particular focus on models related to predicting and controlling pandemics, such as the SIR model. Specifically, we apply this method to solve a six-compartment model
[...] Read more.
The current study aims to utilize the homotopy perturbation method (HPM) to solve nonlinear dynamical models, with a particular focus on models related to predicting and controlling pandemics, such as the SIR model. Specifically, we apply this method to solve a six-compartment model for the novel coronavirus (COVID-19), which includes susceptible, exposed, asymptomatic infected, symptomatic infected, and recovered individuals, and the concentration of COVID-19 in the environment is indicated by , , , , , and , respectively. We present the series solution of this model by varying the controlling parameters and representing them graphically. Additionally, we verify the accuracy of the series solution (up to the -degree polynomial) that satisfies both the initial conditions and the model, with all coefficients correct at 18 decimal places. Furthermore, we have compared our results with the Runge–Kutta fourth-order method. Based on our findings, we conclude that the homotopy perturbation method is a promising approach to solve nonlinear dynamical models, particularly those associated with pandemics. This method provides valuable insight into how the control of various parameters can affect the model. We suggest that future studies can expand on our work by exploring additional models and assessing the applicability of other analytical methods.
Full article
(This article belongs to the Special Issue Dynamical Systems: Theory and Applications in Mathematical Biology)
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Recent Advances in Fractional Calculus
by
Péter Kórus and Juan Eduardo Nápoles Valdés
Axioms 2024, 13(5), 310; https://doi.org/10.3390/axioms13050310 - 8 May 2024
Abstract
This Special Issue of the scientific journal Axioms, entitled “Recent Advances in Fractional Calculus”, is dedicated to one of the most dynamic areas of mathematical sciences today [...]
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(This article belongs to the Special Issue Recent Advances in Fractional Calculus)
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