Article
Mathematics, Applied
Yu-Ming Chu, B. M. Shankaralingappa, B. J. Gireesha, Faris Alzahrani, M. Ijaz Khan, Sami Ullah Khan
Summary: The current research focuses on nano-material suspensions and flow characteristics, particularly in terms of their applications in biomedical rheological models. This study analyzes the radiative flow of Maxwell nanoliquid on a stretching cylinder, taking into account magnetic effect, Stefan blowing, and bioconvection. The results provide insights into the behavior of dimensionless parameters on dimensionless velocity, concentration, and thermal profiles through graphical representations, with significant findings regarding velocity change, thermal and mass relaxation times, Brownian factor, and microorganism concentration.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Tie-Hong Zhao, M. Ijaz Khan, Yu-Ming Chu
Summary: Mixed convection is a heat transport mechanism in thermodynamic systems that involves the motion of fluid particles influenced by both gravity and external forces. This study focuses on the mixed convective flow of Ree-Eyring fluid between two rotating disks, considering the effects of porosity and velocity slip. The energy equation is modeled with various factors such as heat generation/absorption, dissipation, radiative heat flux, and Joule heating. The results obtained are compared with previous studies, showing good agreement. Interesting physical phenomena such as skin friction and heat transfer are also numerically calculated.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Mubbashar Nazeer, Farooq Hussain, M. Ijaz Khan, Asad-ur-Rehman, Essam Roshdy El-Zahar, Yu-Ming Chu, M. Y. Malik
Summary: This article investigates the electro-osmotic flow of non-Newtonian fluid in a micro-channel. Perturbation method is used to obtain the approximate analytical solution and pseudo-spectral collocation method is used to calculate the error in the solution. The study reveals the impact of various parameters on velocity and heat profiles, providing insights for understanding the behavior of non-Newtonian fluid in microchannels.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Fatma A. Hashim, Essam H. Houssein, Kashif Hussain, Mai S. Mabrouk, Walid Al-Atabany
Summary: This paper introduces a new metaheuristic optimization algorithm called Honey Badger Algorithm (HBA), inspired by the intelligent foraging behavior of honey badgers, to develop an efficient search strategy for solving optimization problems. Experimental results demonstrate the effectiveness and superiority of HBA in solving optimization problems with complex search-space.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Applied
Yu-Ming Chu, Seemab Bashir, Muhammad Ramzan, Muhammad Yousaf Malik
Summary: This study examines the impact of unsteady viscous flow in a squeezing channel and investigates the flow and heat transfer mechanism of different shapes of silver-gold hybrid nanofluid particles in the base fluid. The numerical solution and parameter analysis reveal that the Yamada-Ota model of the Hybrid nanofluid has a higher temperature and velocity profile, and the performance of hybrid nanoparticles is superior to that of common nanofluids.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Fang Jin, Zi-Shan Qian, Yu-Ming Chu, Mati Ur Rahman
Summary: The investigation of this research article focuses on studying the dynamical behavior of the drinking population using the CF arbitrary order operator and a special non-singular kernel. The proposed system is analyzed for existence and uniqueness of solution using fixed point theory and Picard's technique. Numerical analysis using the ABM method is also utilized to interpret the approximate results and observe the dynamical behavior corresponding to different fractional orders.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Kulandhivel Karthikeyan, Panjaiyan Karthikeyan, Haci Mehmet Baskonus, Kuppusamy Venkatachalam, Yu-Ming Chu
Summary: This paper focuses on the existence results of psi-Hilfer fractional impulsive integro-differential equations with almost sectorial operators, proving mild solutions using the Schauder fixed-point theorem and measure of noncompactness. Two cases of operators associated semigroup are discussed, along with an abstract application via Hilfer fractional derivative system to verify the results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Salvatore Cuomo, Vincenzo Schiano Di Cola, Fabio Giampaolo, Gianluigi Rozza, Maziar Raissi, Francesco Piccialli
Summary: Physics-Informed Neural Networks (PINN) are a type of neural network that incorporates model equations, such as partial differential equations, as a component. PINNs have been used to solve various types of equations, including fractional equations and stochastic partial differential equations. Current research focuses on optimizing PINN through different aspects, such as activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the demonstrated feasibility of PINN in certain cases compared to traditional numerical techniques, there are still unresolved theoretical issues.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Yihong Zhou, Xiao Zhang, Feng Ding
Summary: This paper investigates the parameter optimization problem of a class of radial basis function-based multivariate hybrid models and proposes a partially-coupled nonlinear parameter optimization algorithm. The algorithm shows low computational complexity and high parameter estimation accuracy through computational efficiency analysis and numerical simulation verification.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Amin Jajarmi, Dumitru Baleanu, Kianoush Zarghami Vahid, Saleh Mobayen
Summary: Research on immunogenic tumor dynamics based on a fractional model involves investigating stability, equilibrium points, and implementing a modified predictor-corrector method. Results show the new model provides flexibility in adjusting complex dynamics and implementing a tracking control method can decrease tumor-cell population development. The satisfaction of control purpose is confirmed by simulation results tracking tumor-free steady state in realistic cases.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Xilin Xin, Yidong Tu, Vladimir Stojanovic, Hai Wang, Kaibo Shi, Shuping He, Tianhong Pan
Summary: This paper proposes a novel online mode-free integral reinforcement learning algorithm to solve multiplayer non-zero sum games. By collecting and learning subsystem information of states and inputs, and using online learning to compute corresponding N-coupled algebraic Riccati equations, the policy iterative algorithm presented in this paper can solve the coupled algebraic Riccati equations of multiplayer non-zero sum games. The effectiveness and feasibility of the design method is verified through a simulation example involving three players.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Muhammad Usman Ashraf, Muhammad Qasim, Abderrahim Wakif, Muhammad Idrees Afridi, Isaac L. Animasaun
Summary: This article numerically examines the peristaltic flow of blood-based nanofluid using the generalized differential quadrature method. It adopts the Casson constitutive model to depict flow characteristics in a uniform wavy tube, and considers the non-Newtonian nature and heat transfer feature of the nanofluidic medium. The study successfully models the flow under realistic assumptions, and explores the effects of adding magnetite nanoparticles in the biofluidic medium.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Xiao-Tian Gao, Bo Tian
Summary: This Letter focuses on the characteristics of water waves in a narrow channel and presents two branches of similarity reductions for the horizontal velocity and elevation of the waves through symbolic computation.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Rajanish Kumar Rai, Subhas Khajanchi, Pankaj Kumar Tiwari, Ezio Venturino, Arvind Kumar Misra
Summary: This paper presents a mathematical model to evaluate the impact of social media advertisements in combating the coronavirus pandemic in India. The study finds that non-pharmaceutical interventions strategies play a key role in reducing the basic reproduction number and controlling disease transmission.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Mathematics, Applied
Abderrahim Wakif, Rachid Sehaqui
Summary: The present numerical investigation focuses on the optimum characteristics of magneto-convection phenomenon in Newtonian nanofluids. The study reveals the influence of convective heating and a uniform through-flow process on the stability of the nanofluids, and provides a mathematical model for the non-homogeneous MHD convective flow. The results indicate that the suction and injection effects have different behaviors on system evolution, and the magnetic Lorentz forces and nanomaterials loading contribute to system stabilization. However, the diameter size of nanoparticles and the thermal Biot number have a destabilizing effect on the nanofluidic medium.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Sayed Allamah Iqbal, Md Golam Hafez, Yu-Ming Chu, Choonkil Park
Summary: Fractional-order derivatives have a long history in mathematical science, while half derivatives are less commonly used in applied science and engineering. This study investigates the relationship between the classic RLC circuit and the Atangana-Baleanu fractional-order derivative, using Lyapunov spectral analysis to determine the circuit's stability and instability. Bifurcation plots and Lyapunov exponents analysis reveal that nonautonomous dynamical systems lead to instability and chaotic states, which can be transformed into stable spiral nodes with the presence of the Atangana-Baleanu fractional-order derivative.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Hayri Metin Numanoglu, Hakan Ersoy, Bekir Akgoz, Omer Civalek
Summary: This study investigates the size-dependent thermo-mechanical vibration analysis of nanobeams by implementing Hamilton's principle and the stress equation of nonlocal elasticity theory. The finite element method is used to solve the eigenvalue problem and derive stiffness and mass matrices. Nonlocal finite element method is emphasized for analyzing the vibration behavior of nanobeams under different boundary conditions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Automation & Control Systems
Xueli Wang, Derui Ding, Xiaohua Ge, Qing-Long Han
Summary: This article investigates a neural network-based control problem for unknown discrete-time nonlinear systems with DoS attacks and an adaptive event-triggered mechanism. A novel adaptive rule and an NN-based observer are constructed to handle the challenges of complex time series, with an iteration adaptive dynamic programming approach proposed to address the control issue effectively. The boundedness of estimation errors and identified errors are discussed using Lyapunov theory.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2022)
Article
Mathematics, Applied
Liaqat Ali, Bagh Ali, Muhammad Bilal Ghori
Summary: This study investigates the fluctuating temperature in a water-based nanofluid with Cattaneo-Christov features and self-motive bioconvective microbes. The excision/accretion of the leading edge is observed. By implementing similarity measures, a set of partial differential equations is transformed into an ordinary differential pattern. The numerical results of the non-linear system of equations are obtained using a finite element technique and Matlab programming. The findings reveal the effects of persuasive parameters on microbes propagation, fluid temperature, the volume fraction of nano-inclusions, and fluid velocity.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Siddhartha Mishra, Roberto Molinaro
Summary: This article focuses on the application of physics-informed neural networks (PINNs) to approximating inverse problems for partial differential equations (PDEs). Specifically, it investigates data assimilation or unique continuation problems and provides rigorous estimates on the generalization error of PINNs for these problems. The study establishes an abstract framework and utilizes conditional stability estimates for the inverse problem to derive the estimate on PINN generalization error, thereby justifying the use of PINNs in this context.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2022)
