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Article
Mathematics, Applied
Zubair Ahmad et al.
Summary: Pine wilt disease, caused by nematodes transmitted by pine sawyer beetles, is deadly for several pine species and can lead to significant ecological and financial losses. This study presents a model of the disease in pine trees, considering the interaction between nematodes, transmitting beetles, and both asymptomatic and symptomatic trees. The dynamics of the disease are analyzed using nonlinear coupled integer order ODEs, and the basic reproduction number is calculated. Sensitivity analysis is conducted for the most sensitive parameters, and numerical results are obtained using MATLAB software. It is observed that reducing the interaction between infected beetles and susceptible trees can greatly reduce the infection, and conclusions are drawn based on the obtained results.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Muhammad Faizan Malik et al.
Summary: In this paper, the knacks of swarming heuristics are utilized for system identification problem of Fr-NARX systems using the PSO algorithm. The Fr-NARX identification model is constructed by incorporating the fractional differential operator and developing a merit function based on the mean square error between the original and estimated responses. The adjustable weights for the Fr-NARX models are tuned using the PSO algorithm for various scenarios, and the outcomes of the system identification tasks validate the efficacy of swarming heuristics.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Saqib Murtaza et al.
Summary: This study investigates the flow of Casson fluid between two vertical parallel plates under the influence of heat generation and a magnetic field, using the novel concept of fractal fractional derivatives. The numerical solution is obtained using the finite-difference technique, and the velocity and thermal field are analyzed through graphical representations.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Interdisciplinary Applications
Zubair Ahmad et al.
Summary: Chemical processes involve protein enzymes as catalysts, and mathematical modeling is a powerful tool for studying the dynamics of such phenomena, with fractional models being more practical for describing complex systems' dynamics. By using classical and fractional models, the study explores the dynamics of cooperative phenomenon and investigates the effects of different parameters on concentration profiles of various species.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Physics, Applied
M. Younis et al.
Summary: This paper studies the exact traveling wave solutions to the nonlinear Dullin-Gottwald-Holm model with the application in shallow-water waves. Various exact solutions in different forms are obtained using the G'/G-expansion method and reccati mapping techniques. 3D plots and corresponding contour graphs are depicted to illustrate the specific forms of the solutions. The effectiveness and convenience of the method for solving other nonlinear partial differential equations are also demonstrated.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2022)
Article
Nanoscience & Nanotechnology
Naveed Khan et al.
Summary: This paper uses newly developed fractal-fractional differential and integral operators to analyze the dynamics of chaotic systems based on image encryption. The problem is modeled using classical order nonlinear, coupled ordinary differential equations and generalized using fractal-fractional differential operators. The highly nonlinear problem is solved using a numerical scheme and the results are presented graphically.
Article
Mathematics, Interdisciplinary Applications
Zeshan Aslam Khan et al.
Summary: The role of recommender systems in the e-commerce industry is to predict users' interests through approximating users' preferences and item characteristics. Efficient recommendations are required to handle the chaos in users' rating patterns, and different fractional gradient-based adaptive algorithms, such as GFSGD, are employed for this purpose. The proposed GFSGD enhances the performance of recommender systems by improving memory effect and ensuring fast convergence speed for higher fractional order values.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Yasir Muhammad et al.
Summary: This article introduces a new fractional particle swarm optimization gravitational search algorithm with entropy evolution (FPSOGSA-EE) for solving reactive power dispatch problems. Experimental results demonstrate the effectiveness of this method in minimizing line losses and voltage deviations.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Multidisciplinary Sciences
Saqib Murtaza et al.
Summary: Numerical simulations of non-linear Casson nanofluid flow in a microchannel using the fractal-fractional flow model were conducted. The study found that a higher electro-kinetic parameter reduces the fluid velocity and that the fractional and classical models can be obtained from the fractal-fractional model by setting the parameters to zero. Additionally, it was observed that the insertion of Cadmium Telluride nanoparticles increased the heat and mass transfer rates.
SCIENTIFIC REPORTS
(2022)
Article
Physics, Multidisciplinary
Farhad Ali et al.
Summary: This study investigates the magnetogasdynamics effect on a two-phase flow of blood and magnetic particles in a cylindrical vessel. The non-Newtonian behavior of blood is considered, and a mathematical model is formulated with partial differential equations. By using fractional time derivatives, the classical time model is extended. The model is then non-dimensionalized using appropriate dimensionless variables. The study reveals that increasing the magnetic parameter H reduces the velocities of blood and particles, which is beneficial for controlling blood flow and bleeding during magnetic therapy and surgeries. The fractional parameter alpha controls the velocities, temperatures, and concentration of both blood and particles.
WAVES IN RANDOM AND COMPLEX MEDIA
(2022)
Article
Mohammad Partohaghighi et al.
International Journal of Applied and Computational Mathematics
(2022)
Article
Computer Science, Artificial Intelligence
Yasir Muhammad et al.
Summary: This paper presents a new computing paradigm based on fractional order comprehensive learning particle swarm optimization for solving the reactive power dispatch problems in power systems. The method is tested and verified to be stable, effective, and reliable.
APPLIED SOFT COMPUTING
(2022)
Article
Mathematics, Interdisciplinary Applications
Naveed Ishtiaq Chaudhary et al.
Summary: A new fractional calculus algorithm incorporating an auxiliary model has been proposed for solving engineering and applied sciences problems related to fractals and nonlinear dynamics. The algorithm shows accuracy, convergence, robustness, and reliability in identifying systems with input nonlinear output error (INOE).
CHAOS SOLITONS & FRACTALS
(2022)
Article
Multidisciplinary Sciences
Jamal Shah et al.
Summary: Gold nanoparticles are widely used as Tracers in laboratories due to their biocompatibility and ability to transport heat energy to tumor cells. This study investigates the magnetohydrodynamic free convection flow of Casson nanofluid in an inclined channel, with blood as the base fluid and gold nanoparticles uniformly dispersed in it. The results show that the fractional Casson fluid model better describes the fluid velocity, temperature, and concentration profiles compared to the classical Casson fluid model, and various physical parameters have been shown to affect the results through graphical figures and tables.
SCIENTIFIC REPORTS
(2022)
Article
Engineering, Multidisciplinary
Zeeshan Ali et al.
Summary: The manuscript presents a qualitative analysis of a mathematical model for COVID-19, which involves a novel fractal-fractional operator and considers both fractional-order q and fractal dimension p. Numerical simulations and stability analyses are conducted to unveil the characteristics of disease transmission dynamics.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Physics, Multidisciplinary
Hayder Natiq et al.
Summary: This study introduces an analysis framework to understand the dynamics of a 3D plasma model, revealing a complex transition from transient chaos to steady periodic behavior. It is shown that by increasing power input, the system can become a multi-stable model with the transition from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Moreover, complexity analyses based on Sample entropy demonstrate that boosting power input can enhance the complexity and randomness of the system's time series by spreading the trajectory in the phase space.
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
Syed T. R. Rizvi et al.
Summary: This study investigates lump and rogue wave interactions with periodic and kink solitons for the generalized unstable space time fractional nonlinear Schrodinger equations using the theory of dynamical systems. Various ansatz transformations are utilized to obtain these solutions, which are then graphically represented in distinct dimensions.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Multidisciplinary
Aly R. Seadawy et al.
Summary: This article investigates the propagation of solitary wave solutions to the Pochhammer-Chree equation, obtaining various types of solutions. The innovative phi(6)-model expansion method is used to extract the solitary wave, and modulation instability analysis is discussed. The obtained outcomes are more general and fresh, demonstrating the effectiveness of the method.
Article
Mathematics, Interdisciplinary Applications
Aly R. Seadawy et al.
Summary: In this research, the double-chain model for DNA is analytically studied using the Phi(6)-model expansion method to extract traveling wave solutions. The results show that the system theoretically has extremely rich exact wave structures of biological relevance.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Materials Science, Multidisciplinary
S. T. R. Rizvi et al.
Summary: This study investigates various forms of optical dromions for a weak time fractional nonlinear Schr?dinger equation with parabolic law. Through different ansatz approaches and specific conditions, the study derives bright dromions, dromions walls, singular dromions, dark in the bright, combined dark bright solitons, and periodic solutions of types 1, 2, and 3. Results are visually presented graphically in different dimensions.
RESULTS IN PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
M. Bilal et al.
Summary: This article presents new exact wave structures for the Gilson-Pickering equation in plasma physics, achieved through innovative integration norms. The solutions demonstrate straightforward, efficient, and concise computational schemes, suitable for studying complex physical phenomena. The results are crucial for understanding wave propagation and for numerical and experimental verification in plasma physics.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
M. Bilal et al.
Summary: This article provides modulation instability analysis and new exact wave solutions for the unidirectional Dullin-Gottwald-Holm (DGH) system, describing wave propagation in shallow water. The exact wave solutions, including shock, singular, and shock-singular forms, are extracted using an innovative integration norm. The constraints for the existence of solutions are discussed, and suitable parameter choices generate three-dimensional and two-dimensional sketches, along with contour plots.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
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Computer Science, Information Systems
Farhad Ali et al.
Article
Mathematics, Interdisciplinary Applications
Abdon Atangana et al.
CHAOS SOLITONS & FRACTALS
(2019)
Article
Physics, Multidisciplinary
Sania Qureshi et al.
EUROPEAN PHYSICAL JOURNAL PLUS
(2019)
Article
Engineering, Mechanical
Marwan Alquran et al.
NONLINEAR DYNAMICS
(2018)
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Zhouchao Wei et al.
CHAOS SOLITONS & FRACTALS
(2018)
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I. Jaradat et al.
CHAOS SOLITONS & FRACTALS
(2018)
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Engineering, Mechanical
Karthikeyan Rajagopal et al.
NONLINEAR DYNAMICS
(2018)
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Physics, Multidisciplinary
S. Vaidyanathan et al.
EUROPEAN PHYSICAL JOURNAL PLUS
(2018)
Article
Physics, Multidisciplinary
Qiang Lai et al.
CHINESE JOURNAL OF PHYSICS
(2018)
Article
Physics, Multidisciplinary
Tomasz Kapitaniak et al.
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Engineering, Mechanical
Guangya Peng et al.
NONLINEAR DYNAMICS
(2017)
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Physics, Multidisciplinary
Mekkaoui Toufik et al.
EUROPEAN PHYSICAL JOURNAL PLUS
(2017)
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Mathematics, Interdisciplinary Applications
B. C. Bao et al.
CHAOS SOLITONS & FRACTALS
(2017)
Article
Mathematics, Interdisciplinary Applications
Abdon Atangana
CHAOS SOLITONS & FRACTALS
(2017)
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Engineering, Mechanical
Akif Akgul et al.
NONLINEAR DYNAMICS
(2016)
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Zhouchao Wei et al.
NONLINEAR DYNAMICS
(2016)
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Mathematics, Applied
Ping Zhou et al.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2014)
Article
Multidisciplinary Sciences
Maolin Du et al.
SCIENTIFIC REPORTS
(2013)
Article
Mathematics, Interdisciplinary Applications
A. Chudzik et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2011)
