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Article
Mathematics, Applied
Kamal Shah et al.
Summary: In this article, we thoroughly study a mathematical model for a novel coronavirus using Caputo fractional derivative. We investigate the existence and uniqueness of the solution to the model using fixed point theorems and establish conditions for stability. Additionally, we analyze the model using the Laplace Adomian decomposition method and validate the results using real data from Pakistan.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Hikmet Koyunbakan et al.
Summary: In this paper, we investigated the inverse nodal problem and stability of the fractional Sturm-Liouville problem. We provided asymptotic forms for the nodal parameters and used them to reconstruct the potential function with a limit of the nodal parameters. We proved the existence of this limit. Furthermore, we showed the wellposedness of the problem in other aspects. We demonstrated that the set of potential functions satisfying the condition integral(pi)(0) q(t)d(alpha)t < infinity is homeomorphic to the space of quasi nodal sequences. The results presented in this paper are different and more general than previous ones as they include the fractional derivative. When alpha = 1, the results coincide with those for the classical derivative problem.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Engineering, Multidisciplinary
Kashif Ali Abro et al.
Summary: This article investigates the chaos control and chaotic characteristics of brushless DC motors using fractal-fractional differentiations. Mathematical modeling and numerical simulations are performed to analyze the stability and performance of the motors. The results are important for improving the stability of brushless DC motors.
INTERNATIONAL JOURNAL OF MODELLING AND SIMULATION
(2023)
Article
Information Science & Library Science
Qizhi He et al.
Summary: This study compares the dynamic characteristics of Chinese and American energy prices, including learning expectation, volatility, and persistence. It determines the suitable learning speeds and calculates energy price expectations using learning models. The study examines volatility characteristics and Granger-spillover effects among different energy prices and expectations using stochastic models. It empirically tests and compares the persistence characteristics and reasons behind Chinese and American energy prices by introducing expectation, volatility, and foreign energy price into the persistence model. Conclusions and suggestions are provided based on the theoretical analysis and empirical results.
JOURNAL OF GLOBAL INFORMATION MANAGEMENT
(2023)
Article
Mathematics, Applied
Bo Li et al.
Summary: This paper presents a novel type of generalized Kopel triopoly model to reveal the complex dynamics and transitions between different dynamic behaviors. The construction process of the model is explained in detail based on microeconomic theory. The existence and stability of fixed points are derived and the corresponding transition processes are presented clearly for some fixed parameters. Numerical simulations are conducted to derive representative orbits, chaotic indicators, Lyapunov exponents, and bifurcation continuation, revealing the complexity of the Kopel triopoly game and corresponding mechanisms.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Zaid Odibat et al.
Summary: In this paper, a new fractional derivative operator using the generalized cardinal sine function as a non-singular analytic kernel is proposed. The corresponding fractional integral operator is also provided. The new fractional operators are expressed as sums in terms of the Riemann-Liouville fractional integral operator. An efficient extension of the new fractional operator, including an integrable singular kernel, is introduced to overcome the initialization problem in related differential equations. A numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives is proposed. The proposed fractional operators, developed relations, and numerical method are expected to contribute to the field of fractional calculus.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Physics, Multidisciplinary
Shaohui Yan et al.
Summary: This paper introduces the concept of fractional calculus into the 5D chaotic system to obtain a new 5D fractional-order chaotic system. The system exhibits multi-scroll hidden attractor and multi-stability. By analyzing various characteristics, it is found that the system is sensitive to parameters and initial values, and can produce different types of attractors with varying parameters.
Article
Mathematics, Applied
Lei Zhang et al.
Summary: This paper explores the effect of time delay on coronavirus transmission and proposes a model solution. By numerical simulation and stability analysis, the reliability and stability of the model are demonstrated.
Article
Mathematics, Interdisciplinary Applications
Dhinakaran Veeman et al.
Summary: This paper presents a novel conservative chaotic oscillator and examines its various dynamics, revealing its unique behaviors such as multistability and symmetric dynamics. The equilibrium points of the oscillator are investigated and analyzed, including bifurcations, Lyapunov exponents, and the Poincare section of its dynamics. The oscillator is also studied from the viewpoint of initial conditions. The research results demonstrate that the oscillator is conservative, dissipateless, and exhibits various dynamics including equilibrium points and chaos, with both stable and unstable fixed points.
Article
Physics, Multidisciplinary
Sayed Saifullah et al.
Summary: In this paper, a new three-dimensional continuous chaotic model based on the modification in the Lorenz system is presented and investigated. The model is analyzed in various aspects, including equilibrium points, stability, dissipation, attractors, bifurcations, and sensitivity. The numerical simulations confirm the chaotic nature of the system. Theoretical and numerical studies show that the model exhibits complex dynamics with certain physical characteristics.
Article
Multidisciplinary Sciences
Jianxiang Yang et al.
Summary: This paper focuses on the finite-time generalized synchronization problem of non-identical fractional order chaotic (or hyper-chaotic) systems by designing an adaptive sliding mode controller. The effects of disturbances and model uncertainties are taken into account. The proposed approach is validated through numerical simulations, and a novel speech cryptosystem is proposed based on the generalized finite-time synchronization criterion.
Article
Mathematics, Applied
Zohreh Eskandari et al.
Summary: A newly disclosed nonstandard finite difference method was used to discretize a prey-predator model, and the critical normal form coefficients of bifurcations for both one-parameter and two-parameter bifurcations were investigated. The model exhibited various local bifurcations such as period-doubling, Neimark-Sacker, and strong resonances. The analysis of critical normal form coefficients revealed the dynamical scenarios corresponding to each bifurcation point. Numerical simulations using Matlab package validated the theoretical analysis and provided ecological insights.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Physics, Multidisciplinary
Adnan Sami et al.
Summary: In this article, a fractional-order mathematical model representing tritrophic interaction amongst plants, herbivores, and carnivores is studied. The existence and uniqueness of the system are investigated, while the stability is studied using stability analysis methods. Numerical calculations and chaos behavior analysis are also conducted.
Article
Mathematics, Applied
Guenyaz Ablay
Summary: The complex dynamic behavior of nuclear reactors is qualitatively described by novel chaotic system models and analyzed using Lyapunov spectra, bifurcation diagrams, and phase diagrams. The study reveals rich bifurcation phenomena and demonstrates the effect of the offset boosting method on system behavior.
Article
Mathematics, Interdisciplinary Applications
Changjin Xu et al.
Summary: This paper presents a theoretical and complex numerical analysis of the 2-torus chaotic system with a power-law kernel. Various dynamical characteristics of the complex system are investigated, including the existence of unique attractors, attractor projection, time series analysis, and sensitivity to initial values. It is observed that coexistence of 4-torus attractors can occur at different fractional orders. The numerical illustrations show that transitioning from higher to lower fractional orders significantly affects the dynamics of the system and shrinks the oscillatory range's geometry. Additionally, new oscillations emerge at lower fractional orders, with lower amplitudes compared to those at higher fractional orders.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Materials Science, Multidisciplinary
Asif Khan et al.
Summary: In this article, the behaviour of the time fractional nonlinear Schrodinger equation under two different operators are investigated. Numerical and analytical solutions are obtained using the modified double Laplace transform. The error analysis shows that the system depends primarily on time, with small errors observed for small time values. The efficiency of the proposed scheme is verified with examples and further analyzed graphically and numerically.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
Shabir Ahmad et al.
Summary: In this article, the HIV-1 infection mathematical model is generalized using a nonsingular fractional operator. The existence and stability of a unique solution to the model under the suggested operator are addressed using Picard-Lindelof and fixed-point theory. Numerical simulations are provided to study the complex dynamics of the model for different fractional orders.
Article
Mathematics, Interdisciplinary Applications
Dhinakaran Veeman et al.
Summary: A novel conservative chaotic oscillator with multistable and symmetric dynamics is examined in this study. The equilibrium points, bifurcations, Lyapunov exponents, and Poincare section of the oscillator's dynamics are analyzed. The oscillator is shown to be conservative, with various dynamics including equilibrium points and chaos.
Article
Mathematics, Applied
Dumitru Baleanu et al.
Summary: This paper investigates the hyperchaos analysis, optimal control, and synchronization of a nonautonomous cardiac conduction system. Various approaches are used to analyze, control, and synchronize the hyperchaotic behaviors, demonstrating the efficacy of proposed strategies through simulation and theoretical justification. The new nonlinear fractional model shows more flexible behavior than its classical counterpart due to its memory effects.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
Bo Li et al.
Summary: In this article, multiple and generic bifurcations of planar discrete-time Hindmarsh-Rose oscillator are investigated in detail using bifurcation theory and numerical continuation techniques. Three kinds of one-parameter bifurcation and five kinds of two-parameter bifurcation are studied, with different critical cases of each bifurcation computed and their possible transitions explored. Particularly, the bifurcations of higher iterations and the bifurcation distributions of two-parameter bifurcation point are observed.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Xiangxin Leng et al.
Summary: This study proposes a fractional-order system based on an existing integer-order system and discovers various dynamic behaviors through numerical simulation. The research results indicate that the dynamic behaviors of the system gradually transition from dissipative to conservative with the increase of order.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Multidisciplinary
Ndolane Sene
Summary: This paper investigates a new fractional-order chaotic system described by the Caputo fractional derivative, analyzing bifurcation maps to detect chaotic regions. A numerical discretization is introduced to depict phase portraits and illustrate the influence of the Caputo derivative order, while Lyapunov exponents play a key role in characterizing chaos. Theoretical results are confirmed through simulation of the circuit representation, showing good agreement between graphical representations and oscilloscope phase portraits.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Engineering, Multidisciplinary
Zain-Aldeen S. A. Rahman et al.
Summary: This paper introduces a new fractional order chaotic system without equilibrium, and investigates its dynamical behaviors through analytical and numerical methods. A synchronization mechanism based on adaptive control theory is developed to synchronize two identical systems, and experimental testing using Arduino Due boards demonstrates the practicality of the system in real-world applications.
Article
Mathematics, Interdisciplinary Applications
Hongyan Jia et al.
CHAOS SOLITONS & FRACTALS
(2020)
Article
Physics, Multidisciplinary
Yue Li et al.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2020)
Article
Engineering, Mechanical
Guoyuan Qi
NONLINEAR DYNAMICS
(2019)
Article
Engineering, Mechanical
Shijian Cang et al.
NONLINEAR DYNAMICS
(2017)
Article
Mathematics
G. M. Mahmoud et al.
MISKOLC MATHEMATICAL NOTES
(2017)
Review
Mathematics, Interdisciplinary Applications
Jay Prakash Singh et al.
CHAOS SOLITONS & FRACTALS
(2016)
