Article
Mathematics, Applied
Suhua Lai, Xinying Xu
Summary: This paper establishes the global existence of strong solutions for planar compressible, viscous, heat-conductive Hall-MHD equations with large initial data by achieving uniform positive lower and upper bounds of the density. The conclusion of Theorem 1.1 is derived based on the bounds of the density and the skew-symmetric nature of the Hall term.
COMMUNICATIONS IN MATHEMATICAL SCIENCES
(2021)
Article
Mathematics, Applied
Rudong Zheng, Boling Guo
Summary: We examine the Cauchy problem of the ideal MHD system with a constant nonzero background magnetic field e, providing a new proof of global existence for small perturbations of an initial stable state (0, e). The proof relies on the null structure of the system and new weighted energy estimates established along the characteristics.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2021)
Article
Mathematics, Applied
Huali Zhang
Summary: This paper discusses the Cauchy problem of the fractional magnetohydrodynamic (MHD) system with the Hall and ion-slip effects, and proves the global existence of solutions for a class of large initial data by exploring the structure of semilinear and quasilinear terms. Both the velocity and magnetic fields can be arbitrarily large in H3 (Double-struck capital R3).
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics
Xiaopeng Zhao
Summary: This paper establishes the algebraic decay rate of solutions and higher-order derivative of solutions for the 3D generalized Hall-MHD system, provided that the L1-norm of initial data is sufficiently small and the parameters lie within certain ranges.
MATHEMATISCHE NACHRICHTEN
(2021)
Article
Mathematics, Applied
Jiahui Fang, Junyu Lin
Summary: In this study, we investigate the flow of compressible biaxial nematic liquid crystal in a bounded domain. We establish the local existence of a unique strong solution using Galerkin's approximation method. Furthermore, we derive a blow up criterion for this local strong solution in terms of blow up of rho Lt infinity BMOx and backward difference nLtrLx infinity+ backward difference mLtrLx infinity for any r>3.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Jiri Neustupa, Minsuk Yang
Summary: The article assumes that Omega is either the whole space R-3, a half-space, or a smooth bounded or exterior domain in R-3; T > 0, and (u, b, p) is a suitable weak solution of the MHD equations in Omega x (0, T). The study shows that if the sum of the L-3-norms of u and b over an arbitrarily small ball B-rho(x(0)) is finite as t approaches t(0)-, then (x(0), t(0)) is a regular point of the solution (u, b, p).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Jun Zhou, Huan Zhang
Summary: This paper investigates a sixth-order Boussinesq equation with dispersive, linear strong damping, and nonlinear source using potential well methods. It focuses on the local well-posedness of solutions, global existence and finite time blow-up conditions at different initial energy levels, establishment of a blow-up condition independent of the potential well depth, and upper bound estimation of blow-up time.
JOURNAL OF NONLINEAR SCIENCE
(2021)
Article
Mathematics, Applied
Chien-Hong Cho, Ying-Jung Lu
Summary: This study investigates the finite difference approximation for axisymmetric solutions of a parabolic system with blow-up. By using uniform temporal grids for the computation of blow-up time and behaviors, limitations of schemes with adaptive temporal increments are overcome. The research also includes numerical analysis of various blow-up behaviors and the comparison between blow-up of exact solution and numerical solution.
Article
Mathematics, Applied
Baoying Du
Summary: In this paper, the authors investigate the 3D incompressible Hall-magnetohydrodynamics with partial dissipation. They establish an improved blow-up criterion for classical solutions based on previous results and also obtain the existence of classical solutions under certain conditions for the initial data.
BOUNDARY VALUE PROBLEMS
(2023)
Article
Mathematics, Applied
Jin Tan
Summary: This study investigates the global existence of finite energy weak solutions to 3D density-dependent magnetohydrodynamics system with Hall-effect in a general smooth bounded domain. By controlling the density range of initial conditions and the constraining nature of the density transport equation, a satisfactory compactness argument for the magnetic field has been achieved.
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(2021)
Article
Mathematics, Applied
Xing Wu, Jinlu Li
Summary: In this paper, the global existence of the three-dimensional generalized incompressible Hall-MHD equations is established for a class of large initial data, using a perturbation argument and fully exploring the nonlinear structure of the system. This result considerably improves upon a recent study by Li et al. on the generalized HallMHD system with different viscosity and magnetic diffusion coefficients.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics, Applied
Alex H. Ardila, Mykael Cardoso
Summary: By using variational methods, the stability and strong instability of ground states for the focusing inhomogeneous nonlinear Schrodinger equation (INLS) have been studied. It has been shown that the ground states are strongly unstable by blow-up when the nonlinearity is L-2-supercritical.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
(2021)
Article
Mathematics, Interdisciplinary Applications
Hang Ding, Jun Zhou
Summary: This paper establishes the local well-posedness of weak solutions for a class of quasilinear wave equations with damping, and investigates their global existence, asymptotic behavior, and finite time blow-up. It also shows that weak solutions with supercritical initial energy may blow up in finite time with arbitrarily high energy, and derives the upper and lower bounds of the blow-up time for blow-up solutions.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Jishan Fan, Yong Zhou
Summary: This paper demonstrates uniform regularity for a density-dependent incompressible Hall-MHD system.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Physics, Multidisciplinary
Andronikos Paliathanasis
Summary: The study investigates the symmetries and transformations of the partial differential equations of the one-dimensional magnetohydrodynamic system, revealing its invariance under a seventh-dimensional Lie algebra. It derives the optimal system and applies Lie invariants to derive similarity transformations, presenting various types of oscillating solutions.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Mathematics
Bashir Ahmad, Ahmed Alsaedi, Mohamed Berbiche, Mokhtar Kirane
Summary: The study investigates the Cauchy problem for a 2 x 2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities, and shows the existence of small data-global solutions and finite time blowing-up solutions based on conditions on exponents and fractional orders. Additionally, the L-infinity-decay estimates of global solutions are investigated.
TAIWANESE JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Zahid Nisar, Tasawar Hayat, Ahmed Alsaedi, Bashir Ahmad
Summary: The current article investigates the magnetohydrodynamic (MHD) radiative peristaltic flow of a couple stress nanoliquid in a symmetric channel. The influences of Joule heating, viscous dissipation, Brownian motion, thermophoresis, and a first-order chemical reaction on the flow characteristics are examined. The findings show that temperature increases with increasing Brownian motion and thermophoresis parameters, while it decreases with radiation variable. The concentration of the fluid decreases for a couple stress fluid variable, and the heat transfer coefficient increases with the Eckert number.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Santosh Biswas, Bashir Ahmad, Subhas Khajanchi
Summary: In this paper, we investigate a predator-prey system with cannibalism and infection. We study the model in presence of delays for the maturation of prey and predator. The local stability and bifurcation analysis around realistic steady states are investigated. Our findings demonstrate the destabilizing effect of maturation delays and the self-regulatory role of cannibalism in controlling disease transmission and stabilizing the oscillations in the system.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
G. Narayanan, M. Syed Ali, Hamed Alsulami, Tareq Saeed, Bashir Ahmad
Summary: This paper proposes a novel approach to solve the synchronization problem of T-S fuzzy fractional-order discrete-time complex-valued genetic regulatory networks. Several effective conditions are derived based on algebraic inequality and complex-valued linear matrix inequalities. Our results are less conservative than existing ones.
NEURAL PROCESSING LETTERS
(2023)
Article
Mathematics
Ahmed Alsaedi, Mokhtar Kirane, Ahmad Z. Fino, Bashir Ahmad
Summary: By using the nonlinear capacity method, some results are obtained regarding the nonexistence of nontrivial solutions to time and space fractional differential evolution equations with transformed space argument. These results are then applied to a 2 x 2 system of equations with transformed space arguments.
BULLETIN OF MATHEMATICAL SCIENCES
(2023)
Article
Mathematics, Applied
Nemat Nyamoradi, Bashir Ahmad
Summary: This work explores the existence of solutions to a new class of boundary value problems, which consist of a system of nonlinear differential equations with generalized fractional derivative operators of different orders and nonlocal boundary conditions containing Riemann-Stieltjes and generalized fractional integral operators. The study emphasizes that the nonlinearities in the system are of general form, depending on both the unknown functions and their lower order generalized fractional derivatives. The uniqueness of the given problem is proved by applying the Banach contraction mapping principle, and the existence of solutions for the given system is demonstrated using Leray-Schauder alternative. Two concrete examples are provided to illustrate the obtained results.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics
Santosh Kumar Sharma, Amar Nath Chatterjee, Bashir Ahmad
Summary: The study focuses on the effects of antiviral therapy on Hepatitis C Virus (HCV) infection. HCV infection damages healthy hepatocyte cells in the liver, leading to cirrhosis and hepatocellular carcinoma. A cell-population model is introduced to understand the long-term dynamics of HCV infection under antiviral drug therapies. The model considers the interactions between susceptible hepatocytes, infected hepatocytes, and HCV to provide a comprehensive understanding of the host dynamics.
Article
Mathematics, Applied
Nattapong Kamsrisuk, Sotiris K. Ntouyas, Bashir Ahmad, Ayub Samadi, Jessada Tariboon
Summary: In this paper, we investigate the existence and uniqueness of solutions to a nonlinear coupled systems of (k,phi)-Hilfer fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions. We make use of the Banach contraction mapping principle to obtain the uniqueness result, while the existence results are proved with the aid of Krasnosel'skii's fixed point theorem and Leray-Schauder alternative for the given problem. Examples demonstrating the application of the abstract results are also presented. Our results are of quite general nature and specialize in several new results for appropriate values of the parameters beta(1), beta(2), and the function ' involved in the problem at hand.
Article
Mathematics, Applied
Pegah Taghiei Karaji, Nemat Nyamoradi, Bashir Ahmad
Summary: In this paper, the SIR model with a nonlinear incidence rate is studied. The disease-free equilibrium E0, the endemic equilibrium E1, and the basic reproduction number R0 of the model are obtained. The local asymptotic stability of E0 is established when R0<1, and the local asymptotic stability of E1 is proved when R0>1. The global stability of the model is studied using Barbalat's lemma. The transcritical bifurcation analysis is investigated by the Sotomayor theorem. The existence of Hopf bifurcation and the sensitivity analysis of the basic reproduction number are checked. Numerical simulations are conducted to support the obtained results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Bashir Ahmad, Shorog Aljoudi
Summary: This article investigates the existence criteria for solutions of a nonlinear coupled system of Hilfer-Hadamard fractional differential equations of different orders complemented with nonlocal coupled Hadamard fractional integral boundary conditions. The desired results are achieved using standard fixed-point theorems. The fixed point approach is highlighted as one of the effective methods to establish the existence results for boundary value problems. Examples illustrating the obtained results are provided.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Ahmed Alsaedi, Hana Al-Hutami, Bashir Ahmad
Summary: In this paper, a new class of nonlinear multi-term impulsive anti-periodic boundary value problems involving Caputo type fractional q-derivative operators of different orders and the Riemann-Liouville fractional q-integral operator is introduced and investigated. The uniqueness of solutions to the given problem is proved with the aid of Banach's fixed point theorem. An existence result for the problem is also obtained by applying a Shaefer-like fixed point theorem. Examples are constructed to illustrate the obtained results.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Automation & Control Systems
Ahmed Alsaedi, Jinde Cao, Bashir Ahmad, Ahmed Alshehri, Xuegang Tan
Summary: This article proposes a distributed adaptive control scheme for second-order leader-following multiagent systems with only position information as output. An auxiliary network is used to estimate unmeasurable velocity information and make the output-based distributed adaptive control protocol effective. The distributed synchronization criteria are established, and the convergence analysis is provided based on the stability theory. Several simulation examples are presented to validate the proposed criteria.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Mathematics, Interdisciplinary Applications
Bashir Ahmad, Manal Alnahdi, Sotiris K. Ntouyas
Summary: In this study, a new notion of nonlocal closed boundary conditions is presented. By applying these conditions, the existence of solutions for a mixed nonlinear differential equation involving a right Caputo fractional derivative operator and left and right Riemann-Liouville fractional integral operators of different orders is discussed. A decent and fruitful approach of fixed point theory is employed to establish the desired results. Examples are provided to illustrate the main findings. The paper concludes with some interesting observations.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Abdelhamid Bensalem, Abdelkrim Salim, Bashir Ahmad, Mouffak Benchohra
Summary: This paper investigates the existence of mild solutions to a non-instantaneous integrodifferential equation using resolvent operators in the sense of Grimmer in Frechet spaces. Sufficient criteria ensuring the controllability of the given problem are presented by utilizing the technique of measures of noncompactness in conjunction with the Darbo's fixed point theorem. An illustrative example is also discussed.
CUBO-A MATHEMATICAL JOURNAL
(2023)
Article
Mathematics, Applied
Sotiris K. Ntouyas, Bashir Ahmad, Cholticha Nuchpong, Jessada Tariboon
Summary: In this paper, we investigate fractional order boundary value problems with nonlocal boundary conditions and consider both single-valued and multi-valued cases. The results for the single-valued case are obtained using fixed point theorems and nonlinear alternative theorems, while for the multi-valued case, we employ the nonlinear alternative theorem for multi-valued maps and the fixed point theorem for multi-valued contractions. Numerical examples are provided to illustrate the theoretical results.
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
