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Article
Mathematics, Applied
Trushit Patel et al.
Summary: This paper investigates a nonlinear partial differential equation describing a long dispersive wave. An approximate analytical solution for the equation is obtained using a fractional reduced differential transform method. The effect of the fractional order on the wave profile is discussed and compared with the exact solution. The results demonstrate the effectiveness and reliability of the proposed method in solving the fractional-order Wu-Zhang system.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Interdisciplinary Applications
Bapin Mondal et al.
Summary: This study focuses on analyzing the stability and local bifurcations of an imprecise prey-predator system under uncertain environment. Theoretical and numerical analyses were conducted to study the dynamics of the proposed imprecise model, leading to some biological implications.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Hasib Khan et al.
Summary: In this article, a mathematical model for Covid-19 in the fractal-fractional sense of operators is studied, focusing on the existence of solution, Hyers-Ulam stability, and computational results. The model is qualitatively analyzed by converting it to an integral form and using iterative convergent sequence and fixed point approach. For the computational aspect, a numerical scheme based on Lagrange's interpolation is developed for the fractal-fractional waterborne model, and interesting results are obtained through a case study.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Automation & Control Systems
Azher M. Abed et al.
Summary: This paper proposes a new trajectory tracking controller for the differential drive mobile robot (DDMR) called the nonlinear neural network fractional-order proportional integral derivative (NNFOPID) controller. An Enhanced Fruit Fly Swarm Optimization algorithm is developed to tune the NNFOPID's parameters. The results show that the proposed NNFOPID controller can effectively track three types of continuous trajectories while minimizing the mean square error and the control energy.
MEASUREMENT & CONTROL
(2022)
Article
Multidisciplinary Sciences
Shiro Hirano
Summary: In this study, we model source time functions using stochastic differential equations and demonstrate that the convolution of two stochastic processes (known as Bessel processes) satisfies several empirical laws of source time functions. This includes non-negativity, finite duration, unimodality, a growth rate proportional to t(3), omega(-2)-type spectra, and the frequency distribution known as the Gutenberg-Richter law. We also speculate that the stress drop rate and fault impedance follow the same Bessel process.
SCIENTIFIC REPORTS
(2022)
Review
Biochemical Research Methods
Pietro Hiram Guzzi et al.
Summary: This article discusses the importance of controlling disease spread and the use of computational tools and models to achieve this. Using COVID-19 as an example, it demonstrates how these models can be used to optimize vaccine prioritization strategies and explores their applicability to other diseases.
BRIEFINGS IN BIOINFORMATICS
(2022)
Article
Engineering, Multidisciplinary
Qura Tul Ain et al.
Summary: This paper investigates the transmission of the MERS-CoV model between the human populace and camels, focusing on camels as the primary source of infection. The study explores the time effect of MERS-CoV disease transmission using a non-linear fractional order and analyzes the qualitative theory and uniqueness of solutions using stability analysis methods.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Materials Science, Multidisciplinary
ChiCuong Vu et al.
Summary: Flexible electronics, a branch of wearable electronics, has attracted extensive research attention for its wide range of applications. However, signal acquisition, processing, and noise suppression remain challenging. Researchers have developed new materials and geometrical designs to optimize the performance of flexible electronics. This paper selectively reviews the progress in flexible electronic development over the past two years from the perspectives of materials and fractal structures, and analyzes the significance of fractal structures for devices and applications. The challenges and opportunities of fractal designs for future research are also summarized.
MATERIALS TODAY PHYSICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Wenmeng Zhou et al.
Summary: This paper reviews the significant progress in fractal analysis on the surfaces of thin films in recent decades, discussing the importance of this method in exploring the mechanism of film growth.
FRACTAL AND FRACTIONAL
(2022)
Review
Acoustics
Chun-Hui He et al.
Summary: The article discusses the application of the homotopy perturbation method in nonlinear vibration theory, focusing on the treatment of non-conservative oscillators, including models like Duffing oscillators and fractional oscillators. The authors heuristically explain the method's specific applications through examples, demonstrating its potential in solving practical problems.
JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL
(2022)
Article
Thermodynamics
Assad Ayub et al.
Summary: This study investigates the chemical process in nanomaterials and its applications, such as water-solubility, octanol-water partition coefficient, melting points, and vapor pressure. The impacts of homogeneous heterogeneous reactions and nanoscale heat transport in inclined magnetized 3-D water-based Hybrid nanofluid are determined. The physical quantities are analyzed through mathematical models, numerical solutions, and statistical analysis presented in graphs and tables.
CASE STUDIES IN THERMAL ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
Zubair Ahmad et al.
Summary: This study investigates the dynamics of a new chaotic system using fractal-fractional differential operators, proving that the model will have at least one and a unique solution. Numerical schemes implemented through MATLAB software reveal results portrayed through various graphs.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Sadiq Al-Nassir
Summary: This paper investigates the dynamics behavior of a fractional-order prey-predator system and its discretization with harvesting, considering logistic growth of prey species and Holling type III functional response. The existence and local stability of all equilibria, as well as their discretization, are determined and analyzed. The discrete model is extended to an optimal control problem for obtaining an optimal harvesting policy, with numerical simulations illustrating the theoretical findings.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Siddra Habib et al.
Summary: This paper demonstrates the use of the fractional He-Laplace method to study a nonlinear coupled system of equations with time fractional derivative. The method is shown to provide an effective and convenient way to obtain solutions in the form of convergent series, without restrictions, and is validated through graphical representation and error estimate.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics, Applied
Mir Sajjad Hashemi et al.
Summary: This paper introduces a generalization of the squared remainder minimization method for solving multi-term fractional differential equations, with a focus on linear equations. Approximate solutions are considered in terms of linearly independent functions, and the problem is transformed into a minimization problem using the Lagrange-multiplier method. The convergence and theoretical investigation of this approach are discussed, and relevant examples are studied to demonstrate the accuracy of the method and compare the results with other methods.
NONLINEAR ANALYSIS-MODELLING AND CONTROL
(2021)
Article
Materials Science, Multidisciplinary
M. Ali Akbar et al.
Summary: The study analyzes various networks and cable signal distribution using the modified Zakharov-Kuznetsov equation as a model governing propagation in electrical transmission lines. Through the modified simple equation and the sine-Gordon expansion methods, stable traveling wave solutions were established, determining voltage and current flow for transmission line design. The methods used simplify the extraction of traveling wave solutions and provide insight into voltage and current distributions in the transmission line.
RESULTS IN PHYSICS
(2021)
Article
Computer Science, Artificial Intelligence
Chengli Zheng et al.
Summary: This study developed a new method for estimating natural gas production and consumption based on the nonhomogeneous grey model, namely, the conformable fractional nonhomogeneous grey Bernoulli model. The new model, applied in predicting future data in North America, is shown to outperform other competitors in forecasting natural gas demand. The research also indicates a steady increasing trend in natural gas production and consumption in the coming years.
APPLIED SOFT COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Ting Jin et al.
Summary: This paper investigates the application of uncertain fractional differential equations in financial market modeling, presenting monotonicity theorems and an uncertain fractional mean-reverting model. Pricing formulas for European and American options are derived based on monotone function and present extreme values and time integral theorems. Numerical schemes are designed and illustrated for different parameters through the predictor-corrector method.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Quan H. Do et al.
Summary: A new effective method utilizing fractional-order Chebyshev wavelets is presented for solving two-dimensional distributed-order fractional differential equations (DOFDEs). An exact formula involving regularized beta functions is provided to determine the Riemann-Liouville fractional integral operator of these wavelets. The method yields accurate results and is supported by numerical examples.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Arzu Ahmadova et al.
Summary: This study presents explicit analytical solutions for families of Langevin differential equations with general fractional orders, incorporating homogeneous and inhomogeneous cases. Novelty lies in applying appropriate norms in the proof of existence and uniqueness theorem, and discussing the application of fractional order Langevin differential equations in electrical circuits. Furthermore, Ulam-Hyers stability of Caputo type fractional Langevin differential equations is investigated, with an example provided to validate the main results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Energy & Fuels
Chong Liu et al.
Summary: A new discrete fractional grey model was developed with the use of quantum genetic algorithm to predict future natural gas consumption in China more accurately, providing reasonable suggestions for associated sectors.
Article
Endocrinology & Metabolism
Marcela Salazar-Viedma et al.
Summary: Hashimoto thyroiditis is a pathology caused by autoimmune destruction of the thyroid gland, where an imbalance between T cells and gut microbiota dysfunction can induce the disease.
Article
Engineering, Electrical & Electronic
M. M. Khader et al.
Summary: In this study, an accurate spectral method is presented to solve fractional models of electrical circuits, including RL, RC, and RLC circuits. By utilizing generalized Legendre polynomials for interpolation, numerical solutions for these models are obtained and compared with exact solutions in numerical examples.
INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
Rachana Shokhanda et al.
Summary: In this paper, the time-fractional two-mode coupled Burgers equation with the Caputo fractional derivative is considered, and the He-Laplace method is applied to find its approximate analytical solution. The method decomposes the equation into a series of linear equations, which can be easily solved through Laplace transform. The step-by-step illustration of the solution process demonstrates the method's effectiveness for fractional differential equations.
FRACTAL AND FRACTIONAL
(2021)
Article
Engineering, Mechanical
Ji-Huan He et al.
Summary: In this study, a governing equation for string axial vibrations with temporal and spatial damping forces is established using the Hamilton principle, which is an extension of the well-known Klein-Gordon equation. The classical homotopy perturbation method is found to be ineffective in analyzing this equation, prompting a modification with an exponential decay parameter. The analysis reveals that the amplitude decays exponentially with the damping parameter, and a frequency equation is established along with a stability condition analysis. The modified homotopy perturbation method proves to be more effective for nonlinear oscillators and successfully overcomes the shortcomings of the classical approach, as evidenced by the excellent agreement between analytical and numerical solutions.
FACTA UNIVERSITATIS-SERIES MECHANICAL ENGINEERING
(2021)
Article
Multidisciplinary Sciences
Noufe. H. Aljahdaly et al.
Summary: A linear damped nonlinear Schrodinger equation (LDNLSE) is derived using a reductive perturbation technique to investigate the properties of dissipative modulated nonlinear dust-acoustic wavepacket in an electron-ion dusty plasma with superthermal electrons and ions, including rogue waves (RWs). The modulational instability of the dissipative envelope structures is studied and the (un)stable domain of the modulated structures is mapped accurately. Numerical solutions of the LDNLSE using Adomian decomposition method (ADM) show the influence of plasma parameters on dissipative RWs, with a focus on superthermal parameters and dust-neutral collisional frequency. Global residual error is estimated to examine the accuracy of the numerical solutions.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE
(2021)
Article
Mathematics, Interdisciplinary Applications
Ziyi Lin et al.
Summary: This paper introduces a fractional-order economic growth model with time delay based on the Solow model, which effectively captures memory characteristics in economic operations. The simulation verifies the model's theoretical results and predicts China's GDP growth trend, emphasizing the urgency of increasing total factor productivity for sustainable growth.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Zidane Baitiche et al.
Summary: The paper proves the existence of extremal solutions for a novel class of psi-Caputo fractional differential equation with nonlinear boundary conditions, utilizing monotone iterative technique and upper and lower solutions. An example with graphical representations is provided to confirm the validity of the main results.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Naveed Anjum et al.
Summary: In this study, the two-scale fractal theory is employed to model the time-fractional tsunami wave on an unsmooth surface. Mass and momentum conservation equations are established in a fractal space, and solved using He's variational iteration method to study the dynamic behavior of tsunami waves and methods of prevention. The research sheds new light on the field of two-scale fluid mechanics.
GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS
(2021)
Article
Mathematics, Applied
Bikramjeet Kaur et al.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2020)
Article
Mathematics, Applied
Shahram Alizadeh et al.
ADVANCES IN DIFFERENCE EQUATIONS
(2020)
Review
Mathematics, Interdisciplinary Applications
Hang Zheng et al.
DISCRETE DYNAMICS IN NATURE AND SOCIETY
(2020)
Article
Mathematics, Interdisciplinary Applications
Nguyen Huy Tuan et al.
CHAOS SOLITONS & FRACTALS
(2020)
Article
Engineering, Marine
Mostafa M. A. Khater et al.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2019)
Article
Physics, Multidisciplinary
Abdon Atangana et al.
EUROPEAN PHYSICAL JOURNAL PLUS
(2018)
Article
Mathematics, Applied
Ricardo Almeida
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2017)
Article
Thermodynamics
Abdon Atangana et al.
Article
Engineering, Multidisciplinary
E.M.E. Zayed et al.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2011)
