Article
Acoustics
Abdullah Gokyildirim, Haris Calgan, Metin Demirtas
Summary: In this study, the chaotic behavior of a 4D memristive Chen system is investigated by taking the order of the system as fractional. The nonlinear behavior of the system is observed numerically by comparing the fractional-order bifurcation diagrams and Lyapunov Exponents Spectra with 2D phase portraits. Two different fractional orders are determined where the system shows chaotic behavior. Furthermore, a single state fractional-order sliding mode controller (FOSMC) is designed to maintain the states of the system on the equilibrium points.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Engineering, Aerospace
Wenjie Qing, Binfeng Pan, Yueyang Hou, Shan Lu, Wenjing Zhang
Summary: In this study, a novel fractional-order sliding mode-based control method was developed for a class of nonautonomous nonlinear systems, using a fractional stability theorem and a fractional-order sliding surface. The applicability and efficiency of the proposed method were demonstrated through simulation results.
Article
Computer Science, Interdisciplinary Applications
Moussa Labbadi, Hassan El Moussaoui
Summary: This paper presents an improved fractional-order fast integral terminal sliding mode control technique to enhance the robustness of a quadrotor unmanned aerial vehicle system against time-varying disturbances. The adopted fractional-order fast integral sliding mode surface ensures finite time convergence, improving the accuracy of attitude and position dynamics.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Computer Science, Artificial Intelligence
Esraa Mostafa, Osama Elshazly, Mohammad El-Bardini, Ahmad M. M. El-Nagar
Summary: An adaptive fractional-order sliding mode control (AFOSMC) is proposed for controlling a nonlinear fractional-order system. This control scheme combines sliding mode control and fractional control to improve the response of nonlinear systems. The proposed AFOSMC includes a fractional-order sliding mode control (FOSMC) and a tuning unit that adjusts the parameters of FOSMC using a Takagi-Sugeno-Kang fuzzy logic system. Stability analysis of the proposed controller is carried out using Lyapunov theorem. The practical implementation of AFOSMC using a microcontroller demonstrates improvements and enhancements in controlling a fractional-order gyroscope system.
Article
Mathematics, Interdisciplinary Applications
Ali Allahem, Anitha Karthikeyan, Manisekaran Varadharajan, Karthikeyan Rajagopal
Summary: The research focuses on computational modeling and investigating nonlinear dynamical changes of a fractional-order chemical reactor system. The use of chaos theory in quantifying nonlinear behaviors and the benefits of Caputo's definition for formulating the fractional-order model are highlighted. The stability of the system for different parameter values is investigated and significant parameter values are identified. The importance of fractional-order treatment and the effectiveness of an adaptive sliding mode controller are emphasized.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Interdisciplinary Applications
Yunmei Fang, Siyang Li, Juntao Fei
Summary: In this study, a second-order sliding mode control (SOSMC) with a fractional module using an adaptive fuzzy controller is developed for an active power filter (APF). A second-order sliding surface using a fractional module is designed to reduce discontinuities and chattering, ensuring system stability and simplifying the design process. Additionally, a fuzzy logic control is employed to estimate parameter uncertainties. Simulation and experimental results demonstrate the effectiveness of the designed fractional SOSMC with adaptive fuzzy controller in satisfactorily eliminating harmonics, as well as its good robustness and stability compared to an integer order controller.
FRACTAL AND FRACTIONAL
(2022)
Article
Computer Science, Information Systems
Abdul-Wahid A. Saif, Khaled Bin Gaufan, Sami El-Ferik, Mujahed Al-Dhaifallah
Summary: This research proposes the implementation of two advanced controllers with integer and fractional order quadrotor systems to enhance control performance, robustness, and accuracy. MATLAB simulation studies verify the effectiveness of the approach, showing that the fractional order quadrotor system outperforms the traditional integer order system. The study highlights the potential of fractional order modeling and control techniques in improving quadrotor system performance, with implications for modern control engineering.
Article
Multidisciplinary Sciences
Alireza Jafary Fesharaki, Mohammad Tabatabaei
Summary: An adaptive fractional-order sliding mode controller is designed for an inverted pendulum-cart system. With a hierarchical sliding mode control approach and novel fractional-order sliding surfaces, the controller stabilizes the system and adjusts the cart position and pendulum angle to zero.
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
(2022)
Article
Mathematics, Interdisciplinary Applications
Chandrali Baishya, R. N. Premakumari, Mohammad Esmael Samei, Manisha Krishna Naik
Summary: This study investigates the chaos behavior of the Bloch equation under the influence of the Caputo fractional derivative, with and without delay, using a sliding mode controller. The presence of chaos in the system is demonstrated through the calculation of Lyapunov exponents for various fractional derivatives, and theoretical assertions are verified through numerical simulations.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Materials Science, Multidisciplinary
F. M. Allehiany, Emad E. Mahmoud, Lone Seth Jahanzaib, Pushali Trikha, Hammad Alotaibi
Summary: The manuscript introduces the dynamics of fractional order neural network under electromagnetic radiation, showing high sensitivity to external stimuli and improvement in neural functioning under the right amount of electromagnetic radiations. Control of chaos in the studied dynamical system around its unique stagnation point using SMC controllers in the presence of uncertainties and disturbances is also explored. These results could provide insights into neuron related problems.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Electrical & Electronic
Yanling Lv, Yuchen Zhang, Qi Liu, Shuo Wang, Dalei Shi
Summary: This paper establishes a fourth-order power system dynamic model and a two-parameter fourth-order power system mathematical model with load reactive power and mechanical input power as chaotic parameters, and explores the mechanism and characteristics of chaos in the power system using chaos theory. A sliding mode controller is designed to suppress the chaotic oscillation of the power system.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2022)
Article
Engineering, Mechanical
Hoang Manh Cuong, Hoang Quoc Dong, Pham Van Trieu, Le Anh Tuan
Summary: This study presents an adaptive robust control system for rubber-tired gantry (RTG) cranes using fractional calculus combined with sliding mode control to deal with parametric variations and unknown wind disturbances. Simulation and experiment results demonstrate the superiority of the proposed control system in tracking actuated states and stabilizing unactuated states, despite uncertainties and disturbances.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Engineering, Civil
Kang Xu, Liping Chen, Antonio M. Lopes, Mingwu Wang, Xiaochuan Li
Summary: A novel robust adaptive fuzzy variable fractional-order sliding mode control strategy is proposed to suppress earthquake-induced vibrations on uncertain building structures. The strategy combines the concepts of variable fractional-order calculus and sliding mode control to establish a new variable fractional-order sliding mode controller. The controller utilizes VFO fuzzy logic with online adaptive approximation to ensure robustness and superior performance in the presence of uncertain structure parameters and external unknown earthquake excitation.
ENGINEERING STRUCTURES
(2023)
Article
Automation & Control Systems
Shixi Hou, Cheng Wang, Yundi Chu, Juntao Fei
Summary: This paper proposes an adaptive fractional-order terminal sliding mode control scheme combined with a recurrent meta-cognitive fuzzy neural network for robust current control of active power filter, which achieves precise tracking performance and superior control performance.
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL
(2022)
Article
Mathematics, Interdisciplinary Applications
Majid Roohi, Chongqi Zhang, Mostafa Taheri, Andreas Basse-O'Connor
Summary: This work proposes a dynamic-free adaptive sliding mode control methodology for synchronizing a specific class of chaotic delayed fractional-order neural network systems in the presence of input saturation. The methodology effectively overcomes the inherent chaotic behavior exhibited by the delayed systems to achieve synchronization by incorporating the frequency distributed model and fractional Lyapunov stability theory.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Hamdy I. Abdel-Gawad, Nasser H. Sweilam, Seham M. Al-Mekhlafi, Dumitru Baleanu
Summary: In this article, an approach for finding the exact solution of the fractional Fokker-Planck equation is presented. The solution is obtained by transforming the equation and implementing the extended unified method. The results show that the solution is a bi-Gaussian distribution, and the friction coefficient has a significant impact on reducing the standard deviation. Moreover, the influence of the fractional derivative is found to be stronger than that of the fractal derivative, and a mixed-Gaussian solution is obtained.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
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
Mathematics, Applied
Mustafa Inc, Talat Korpinar, Zeliha Korpinar, Dumitru Baleanu, Ridvan Cem Demirkol
Summary: This paper examines the new evolution of polarized light ray by optical fiber in the pseudohyperbolic space H-0(2). It gives the characterization of the parallel transportation law associated with the geometric pseudohyperbolic phase of the light ray, defines the principle nature of electric and magnetic field along with the light ray in the pseudohyperbolic space H-0(2) by the geometric invariants, and successfully derives the optical solutions of nonlinear pseudohyperbolic Schrodinger's equations governing the propagation of electromagnetic fields using the traveling wave hypothesis approach.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Acoustics
Asiyeh Ebrahimzadeh, Raheleh Khanduzi, Samaneh P. A. Beik, Dumitru Baleanu
Summary: This paper focuses on exploiting a comprehensive mathematical model for a class of systems with fractional optimal control problems. By applying different optimization algorithms, the most excellent solution for the fractional optimal control problems is obtained.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Mathematics, Applied
Ioannis Dassios, Taulant Kerci, Dumitru Baleanu, Federico Milano
Summary: This article introduces a generalized system of differential equations of fractional-order to incorporate memory into an electricity market model. The study constructs a fractional-order dynamical model to study solutions and provides closed formulas of solutions. The proposed model is compared with a conventional, integer-order electricity market model through an application example and numerical analysis.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Mohammad Prawesh Alam, Arshad Khan, Dumitru Baleanu
Summary: In this paper, a high-order numerical method is studied to approximate multi-term time-fractional diffusion equations. The method is shown to be stable and convergent, and its accuracy and efficiency are validated through numerical simulations.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2023)
Article
Automation & Control Systems
Muhammad Tariq Ali, Dumitru Baleanu, Muhammad Rafiq, Jan Awrejcewicz, Nauman Ahmed, Ali Raza, Muhammad Sajid Iqbal, Muhammad Ozair Ahmad
Summary: Human immunodeficiency viruses are lentiviruses that infect humans and can cause acquired immunodeficiency syndrome. These viruses likely originated from chimpanzees in Central Africa and have spread across Africa and later to other parts of the world. The study examines the effect of immigrants on HIV/AIDS dynamics and proposes a non-standard finite difference method as a numerical solution for modeling the disease.
INTELLIGENT AUTOMATION AND SOFT COMPUTING
(2023)
Article
Mathematics, Applied
Manisha Krishna Naik, Chandrali Baishya, Pundikala Veeresha, Dumitru Baleanu
Summary: Investigation of the dynamical behavior related to environmental phenomena, such as global warming, has been the focus of research. In this study, a model connecting the ACT-like model to three climatic components was analyzed using a Caputo fractional differential equation. Two sliding mode controllers were derived to control chaos in the system, and their influences were analyzed in the presence of uncertainties and external disturbances. A new controlled system of equations without and with uncertainties and external disturbances was obtained, and the global stability of these new systems was established. Numerical simulations were performed to confirm the theoretical claims about the influence of the controller on the system.
Article
Mathematics, Interdisciplinary Applications
Nguyen Duc Phuong, Luu Vu Cam Hoan, Dumitru Baleanu, Anh Tuan Nguyen
Summary: In this paper, the authors investigate a terminal value problem for stochastic fractional diffusion equations with Caputo-Fabrizio derivative. The stochastic noise considered here takes value in the Hilbert space W. The main contribution is the study of well-posedness and ill-posedness of the problem under different smoothness conditions of the Hilbert scale space W' (a subspace of W). They find that the problem is well-posed when W' is sufficiently smooth and ill-posed when a certain parameter is smaller, leading to the construction of a regularization result.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Applied
M. A. Abdelkawy, E. M. Soluma, Ibrahim Al-Dayel, Dumitru Baleanu
Summary: A numerical investigation is conducted in this paper for a class of Riesz space-fractional nonlinear wave equations (MD-RSFN-WEs). The presence of a spatial Laplacian of fractional order, described by fractional Riesz derivatives, is considered in the model. The fractional wave equation governs the mechanical diffusive wave propagation in viscoelastic medium with power-law creep and provides a physical understanding of this equation in the context of dynamic viscoelasticity. A totally spectral collocation approach is used to deal with the independent variables, and the results demonstrate that the spectral scheme is exponentially convergent.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Mechanical
Reetika Chawla, Komal Deswal, Devendra Kumar, Dumitru Baleanu
Summary: In this study, we investigated the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative known as the Atangana-Baleanu Caputo derivative. A stability analysis of the linearized time-fractional Burgers' difference equation was also conducted. All linearization strategies used to solve the proposed nonlinear problem were found to be unconditionally stable. Two numerical examples were considered to support the theory. Additionally, numerical results compared the different linearization strategies and demonstrated the effectiveness of the proposed numerical scheme in three distinct ways.
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2023)
Article
Computer Science, Hardware & Architecture
Sonal Kumari, Karan Singh, Tayyab Khan, Mazeyanti Mohd Ariffin, Senthil Kumar Mohan, Dumitru Baleanu, Ali Ahmadian
Summary: This paper introduces an adaptive continuous authentication approach, a behavioral-based mobile authentication mechanism. It promises to enhance mobile phone security and reduce the burden of password memorization for users.
MOBILE NETWORKS & APPLICATIONS
(2023)
Article
Engineering, Mechanical
Marwan Alquran, Tukur Abdulkadir Sulaiman, Abdullahi Yusuf, Ali S. Alshomrani, Dumitru Baleanu
Summary: This work establishes lump periodic and exact traveling wave solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation using the Hirota bilinear method and robust integration techniques. The innovative solutions provide insights into specific physical difficulties and have proven useful in long-wave and high-power communications networks. The results depict new features and reflect previously unknown physical dynamics for the governing model.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Multidisciplinary
Sanjay Bhatter, Kamlesh Jangid, Shyamsunder Kumawat, Sunil Dutt Purohit, Dumitru Baleanu, D. L. Suthar
Summary: In this study, we investigated calcium fluctuations in cellular environments using the Hilfer fractional advection-diffusion equation. We simulated calcium signalling with different buffers, including calcium-binding buffers, and set limits and start conditions. The results showed that the modified Hilfer calcium model, considering time, position, and the Hilfer fractional derivative, provided a richer physical explanation than the classical calcium model.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Dumitru Baleanu, Mehran Namjoo, Ali Mohebbian, Amin Jajarmi
Summary: The present paper presents a numerical solution for the Ito type stochastic parabolic equation with a time white noise process using a stochastic finite difference scheme. An implicit stochastic finite difference scheme is proposed for this equation, and its mathematical analysis is discussed. Numerical results are compared with the exact solution to evaluate the accuracy and efficacy of the proposed technique.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
