Article
Mathematics, Applied
Jiabin Xu, Hassan Khan, Rasool Shah, A. A. Alderremy, Shaban Aly, Dumitru Baleanu
Summary: The research paper presents an efficient technique for solving fractional-order nonlinear Swift-Hohenberg equations related to fluid dynamics, showing that the Laplace Adomian decomposition method requires minimal calculations and produces solutions in close agreement with other existing methods. Numerical examples confirm the validity of the suggested method, demonstrating its almost identical solutions with various analytical methods through graphs and tables.
Article
Mathematics, Applied
Lazhar Bougoffa, Randolph C. Rach
Summary: This paper explores an interesting variation of the modified decomposition method to determine the solutions of nonlinear initial-boundary value problems for second-order ordinary differential equations found in physics, such as the Thomas-Fermi, Bratu, and Troesch equations.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Mathematics, Interdisciplinary Applications
Hegagi Mohamed Ali, Hijaz Ahmad, Sameh Askar, Ismail Gad Ameen
Summary: In this study, a modified method is proposed to solve nonlinear systems of fractional-order partial differential equations, and it is applied to some important fractional-order nonlinear systems. The results show that the used methods can efficiently and reliably obtain approximate solutions.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics
Muhammad Nadeem, Mouad M. H. Ali
Summary: This paper presents a numerical scheme for solving the nonlinear gas dynamic equation. The authors combine the Laplace-Carson transform with the homotopy perturbation method (HPM) to obtain a series solution of the equation. The results show that this hybrid approach is highly accurate and converges smoothly to the exact solution. Additionally, the authors utilize HPM with He's polynomial to minimize numerical simulations in nonlinear conditions, making the implementation of Laplace-Carson transform easier. They also provide graphical solutions to demonstrate the reliability and convenience of this approach for linear and nonlinear challenges.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Oswaldo Gonzalez-Gaxiola, Anjan Biswas, Yakup Yildirim, Luminita Moraru
Summary: This paper presents a numerical simulation of highly dispersive optical solitons in birefringent fibers with polynomial nonlinear form for the first time. The Laplace-Adomian decomposition scheme is used for the algorithmic approach. Dark and bright soliton simulations are shown with very low error measure, making them almost exact replicas of the analytically derived solitons from the governing system. The suggested iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions.
Article
Mathematics, Applied
Gulalai, Shabir Ahmad, Fathalla Ali Rihan, Aman Ullah, Qasem M. Al-Mdallal, Ali Akgul
Summary: The focus of this manuscript is to analyze the new nonlinear time-fractional (2+1)-dimensional modified KdV equation involving the Atangana-Baleanu Caputo (ABC) derivative. The Laplace Adomian decomposition method (LADM) is applied to extract a semi-analytical solution, and the fixed point theory is used to derive results regarding the existence and uniqueness of solutions. Graphical representations confirm that the ABC operator produces better dynamics, and a comparison between different operators shows that the ABC operator outperforms the Caputo-Fabrizio operator.
Article
Thermodynamics
Abdelazizi Mennouni, Lazhar Bougoffa
Summary: The paper presents a new recursive scheme by combining the Adomian decomposition method with a magnificent recurrence formula to solve the initial-value problem of the general fractional differential equation of the nonlinear Lienard's equation. The proposed method offers advantages in computing and converges swiftly and accurately.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2022)
Article
Computer Science, Interdisciplinary Applications
Umesh, Manoj Kumar
Summary: In this work, a powerful method for solving non-linear singular boundary value problems, known as the advanced Adomian decomposition method, is introduced. This method discusses the use of boundary conditions to obtain coefficient of approximate series solution, provides convergence analysis, error bound, and illustrates high precision approximations with a large effective region of convergence. Examples are considered to demonstrate the robustness and effectiveness of the proposed method.
ENGINEERING WITH COMPUTERS
(2021)
Article
Multidisciplinary Sciences
Diego Caratelli, Paolo Emilio Ricci
Summary: Bell's polynomials can be used to approximate the Laplace Transform of composite functions and higher-order nested functions. The article introduces an extension of Bell's polynomials for representing the derivatives of multiple nested functions. Worked examples are provided, and the polynomials used are reported in the appendices.
Article
Materials Science, Multidisciplinary
Sayed Saifullah, Amir Ali, Kamal Shah, Chanon Promsakon
Summary: This article focuses on the study of the Drinfeld-Sokolov-Wilson equation in the fractal-fractional sense with exponential decay and Mittag-Leffler type kernels. The Laplace transform combined with the Adomian decomposition method is used to obtain the general solution of the system in series form, and the convergence of the obtained solution is also analyzed. Numerical example results demonstrate the impact of the fractal and fractional parameters on the soliton and solitary wave solutions of the system.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
Sonali Kaushik, Saddam Hussain, Rajesh Kumar
Summary: The aggregation and breakage equations have many applications in different fields of science, prompting researchers to find accurate methods to solve them. Due to their complexity, exact solutions are only possible for certain parameters. Therefore, numerical and semi-analytical approaches have been explored to obtain solutions for physically relevant kernels. However, numerical methods often make unrealistic assumptions, leading to the development of semi-analytical methods. In this article, the authors introduce novel and accurate semi-analytical techniques for solving the pure aggregation and breakage equations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Abd Ullah, Aman Ullah, Shabir Ahmad, Imtiaz Ahmad, Ali Akgul
Summary: This paper investigates the complex population dynamical model under the fuzzy Caputo fractional derivative. By employing fuzzy Laplace transform and Adomian decomposition, general numerical results for the proposed model are obtained, and two examples are provided to support the proposed procedure.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Ming-Xian Lin, Chia-Hsiang Tseng, Chao Kuang Chen
Summary: This paper presents the use of Laplace Adomian decomposition method (LADM) to investigate deformation and nonlinear behavior of large deflection problems on Euler-Bernoulli beam, with LADM showing better results compared to ADM due to its rapid convergence and accuracy.
ENGINEERING COMPUTATIONS
(2022)
Article
Mathematics, Applied
Said Mesloub, Huda Alsaud
Summary: This article uses the q-homotopy analysis transformation method (q-HATM) to numerically solve a fractional initial-boundary value problem (IBVP) subjected to an integral condition. The resulting numerical scheme is applied to several test examples, where an exact solution is obtained, to demonstrate its efficiency.
Article
Mathematics, Interdisciplinary Applications
Muhammad Usman, Hussam Alrabaiah, Hidayat ullah Khan, Muhammad Roman
Summary: This study investigated the utility and efficiency of Natural Transform coupled with Adomian Decomposition Method (NADM) for solving differential equations. The results showed that this method is simple, easy to use, and efficient.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Emile F. Doungmo Goufo, Y. Khan, I. Tchangou Toudjeu
Summary: This paper discusses the applications of fractal structures in engineering and introduces a relatively new operator called fractal-fractional derivative (FFD). Through analysis and numerical solutions, the study explores the application of FFD on the third cover of the proto-Lu system and observes the self-replication of attractors in a fractal structure.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Chemistry, Multidisciplinary
Yasir Khan, Safia Akram, Alia Razia, Anwar Hussain, H. A. Alsulaimani
Summary: This study investigated the impact of double diffusive convection and inclined magnetic field in nanofluids on the peristaltic pumping of fourth grade fluid in non-uniform channels. A mathematical model along with analytical techniques were used to calculate the effects of different physical parameters on flow quantities. Results showed that an increase in Brownian motion led to an increase in nanoparticle density, while an increase in thermophoresis decreased fluid viscosity and lowered the fraction of less dense nanoparticles.
Article
Physics, Multidisciplinary
Y. Khan, Afraz Hussain Majeed, Muhammad Afraz Rasheed, A. Alameer, Hasan Shahzad, Sadia Irshad, N. Faraz
Summary: This study investigates the flow attributes of micro-polar non-Newtonian liquid over stretching/shrinking surfaces, and examines the effects of flow parameters such as velocity, temperature, and concentration distribution. The research findings were compared with previous results, and it was observed that the local skin friction coefficient and local Nusselt number amplitude increase with the increase in micro-pole parameters.
FRONTIERS IN PHYSICS
(2022)
Article
Physics, Multidisciplinary
Y. Khan, Rashid Mahmood, Afraz Hussain Majeed, Sadia Irshad, A. Alameer, N. Faraz
Summary: This article numerically investigates the combined convection flows in a cavity with a square cylinder at the center, examining the impact of different parameters on the flow characteristics.
FRONTIERS IN PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Ji-Huan He, Man-Li Jiao, Khaled A. Gepreel, Yasir Khan
Summary: This paper reveals the effectiveness of the homotopy perturbation method for strongly nonlinear oscillators. A generalized Duffing oscillator is adopted to illustrate the solving process step by step. A nonlinear frequency-amplitude relationship with a relative error of 0.91% is obtained, and the solution morphology is discussed along with the improvement of accuracy.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Physics, Multidisciplinary
Naeem Faraz, Afraz Hussain Majeed, Asif Mehmood, Haseeba Sajad, Y. Khan
Summary: The goal of this investigation is to comprehensively analyze hydrodynamic forces during power-law fluid flow across cylinders with different gap considerations. The Galerkin finite element method was used to discretize the system of equations, and simulations were conducted with varied flow behavior index, gap aspects, and Reynolds number. The study found that shear-thickening behavior has a significant impact on drag characteristics and increases the drag coefficient of upstream obstacles due to wider gap spacing.
FRONTIERS IN PHYSICS
(2023)
Article
Mathematics, Applied
Muhammad Tahir, Yasir Khan, Adeel Ahmad
Summary: The main goal of this article is to investigate the effects of pseudoplastic and dilatants behavior of non-Newtonian based nanofluid on peristaltic motion in an asymmetric tapered channel. The study uses Buongiorno's nanofluid model to investigate the heat and mass transfer analysis. The Reiner-Philippoff fluid model is considered to depict the non-Newtonian characteristics of the fluid, which shows interesting behavior for two limiting shear stress cases.
Article
Mathematics, Applied
Imran Siddique, Yasir Khan, Muhammad Nadeem, Jan Awrejcewicz, Muhammad Bilal
Summary: This investigation explores the influence of fuzzy nanoparticle volume fraction on heat transfer of second-grade hybrid Al2O3 +Cu/EO nanofluid over a stretching/shrinking Riga wedge. Flow simulations are conducted using modified Hartmann number, boundary wall slip and heat convective boundary condition. The findings show that the hybrid nanofluid exhibits a higher heat transfer rate compared to nanofluids.
Article
Physics, Applied
Rashid Mahmood, Afraz Hussain Majeed, Asif Mehmood, Imran Siddique
Summary: This study presents the flow behavior of viscoplastic materials in a channel driven-cavity using the Bingham constitutive equation with the modification proposed by Papanastasiou. A model consisting of coupled nonlinear partial differential equations is used to represent the system. The governing equations are nondimensionalized and the computations are carried out using the finite element method. The drag and lift values on a cylindrical obstacle and the pressure drop values across a square obstacle are computed and tabulated for different Bingham numbers.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Mathematics, Applied
Bahram Jalili, Amirhossein Rezaeian, Payam Jalili, Davood Domeri Ganji, Yasir Khan
Summary: The transient squeezing flow of 2D Magnetohydrodynamics (MHD) considering Casson fluid in the existence of solar irradiance is numerically and theoretically clarified. The presence of squeezed numbers plays a crucial role, and an increase in the squeezing factor boosts the temperature of non-Newtonian fluid about 20%. The higher quantities of floating viscosity remarkably affect skin friction, and an increase in the chemical reaction rate diminishes the mass concentration profile. The study of energy transition in solar irradiance process is important for minimizing energy utilization in solar units.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Article
Multidisciplinary Sciences
Yasir Khan, Maria Athar, Safia Akram, Khalid Saeed, Alia Razia, A. Alameer
Summary: The current study investigates the effect of partial slip conditions on double diffusion convection in an asymmetric channel using the inclined magnetic flux of peristaltic flow on Ellis nanofluid model. The fundamental differential equations are solved with lubrication approximation to obtain a coupled system of ordinary differential equations. Numerical solutions and graphical representations are used to understand the flow quantity data. The knowledge gained from this study will be helpful for developing intelligent magneto-peristaltic pumps for specific heat and medication delivery phenomena.
Article
Materials Science, Multidisciplinary
Maria Athar, Adeel Ahmad, Yasir Khan
Summary: The purpose of this article is to explore the fusion of dust particles and polymers in a viscous liquid. The study focuses on the steady laminar flow and heat transportation of a polymeric dusty liquid induced by a uniformly heated, penetrable, and stretchable surface inside the boundary layer. The effects of polymer concentration and Weissenberg number on heat transfer rate and skin friction are analyzed.
MULTIDISCIPLINE MODELING IN MATERIALS AND STRUCTURES
(2023)
Article
Mathematics, Interdisciplinary Applications
Soh Edwin Mukiawa, Yasir Khan, Hamdan Al Sulaimani, McSylvester Ejighikeme Omaba, Cyril Dennis Enyi
Summary: In this study, we analyze a thermal-Timoshenko-beam system with suspenders and Kelvin-Voigt damping type, considering the heat governed by Cattaneo's law. By utilizing semi-group theory and energy method, we establish the existence and uniqueness of a weak global solution, along with an exponential stability result. These results are derived without imposing the equal-wave speed of propagation condition.
FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS
(2023)
Article
Metallurgy & Metallurgical Engineering
Amirali Shateri, Mojgan Mansouri Moghaddam, Bahram Jalili, Yasir Khan, Payam Jalili, Davood Domiri Ganji
Summary: In this study, the influence of a uniform magnetic field on natural convection heat transfer in nanofluids flowing between two infinite parallel plates is examined using the differential transform and Akbari-Ganji methods. The effects of various primary parameters are investigated, and the governing equations are solved with specific boundary conditions. The findings reveal that increasing the squeeze number leads to a decrease in velocity, while increasing the Hartmann number has a similar effect. Moreover, temperature rises with increasing Hartmann number, Eckert number, and thermophoretic parameters, and is directly proportional to Prandtl number. The study compares the efficiency of Akbari-Ganji and differential transform methods for solving nonlinear differential equations, and demonstrates that the former requires fewer computational steps and less time.
JOURNAL OF CENTRAL SOUTH UNIVERSITY
(2023)
Article
Mathematics, Applied
Yasir Khan, Sohaib Abdal, Sajjad Hussain, Imran Siddique
Summary: The evaluation of compact heat density gadgets requires effective measures for heat transportation. In this study, the enhancement of thermal transportation in hybrid nanofluids consisting of water and ethyl glycol with the dispersion of three different nano-entities was investigated. The fluids were transported through a porous medium over a permeable elongating sheet. The results showed that the velocity decreased with the magnetic field parameter and porosity parameter, while the temperature varied among the different hybrid species.
Article
Engineering, Multidisciplinary
A. A. Aganin, A. I. Davletshin
Summary: A mathematical model of interaction of weakly non-spherical gas bubbles in liquid is proposed in this paper. The model equations are more accurate and compact compared to existing analogs. Five problems are considered for validation, and the results show good agreement with experimental data and numerical solutions. The model is also used to analyze the behavior of bubbles in different clusters, providing meaningful insights.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Hao Wu, Jie Sun, Wen Peng, Lei Jin, Dianhua Zhang
Summary: This study establishes an analytical model for the coupling of temperature, deformation, and residual stress to explore the mechanism of residual stress formation in hot-rolled strip and how to control it. The accuracy of the model is verified by comparing it with a finite element model, and a method to calculate the critical exit crown ratio to maintain strip flatness is proposed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Shengwen Tu, Naoki Morita, Tsutomu Fukui, Kazuki Shibanuma
Summary: This study aimed to extend the finite element method to cope with elastic-plastic problems by introducing the s-version FEM. The s-version FEM, which overlays a set of local mesh with fine element size on the conventional FE mesh, simplifies domain discretisation and provides accurate numerical predictions. Previous applications of the s-version FEM were limited to elastic problems, lacking instructions for stress update in plasticity. This study presents detailed instructions and formulations for addressing plasticity problems with the s-version FEM and analyzes a stress concentration problem with linear/nonlinear material properties.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bo Fan, Zhongmin Wang
Summary: A 3D rotating hyperelastic composite REF model was proposed to analyze the influence of tread structure and rotating angular speed on the vibration characteristics of radial tire. Nonlinear dynamic differential equations and modal equations were established to study the effects of internal pressure, tread pressure sharing ratio, belt structure, and rotating angular speed on the vibration characteristics.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
X. W. Chen, Z. Q. Yue, Wendal Victor Yue
Summary: This paper examines the axisymmetric problem of a flat mixed-mode annular crack near and parallel to an arbitrarily graded interface in functionally graded materials (FGMs). The crack is modeled as plane circular dislocation loop and an efficient solution for dislocation in FGMs is used to calculate the stress field at the crack plane. The analytical solutions of the stress intensity factors are obtained and numerical study is conducted to investigate the fracture mechanics of annular crack in FGMs.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xumin Guo, Jianfei Gu, Hui Li, Kaihua Sun, Xin Wang, Bingjie Zhang, Rangwei Zhang, Dongwu Gao, Junzhe Lin, Bo Wang, Zhong Luo, Wei Sun, Hui Ma
Summary: In this study, a novel approach combining the transfer matrix method and lumped parameter method is proposed to analyze the vibration response of aero-engine pipelines under base harmonic and random excitations. The characteristics of the pipelines are investigated through simulation and experiments, validating the effectiveness of the proposed method.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xiangyu Sha, Aizhong Lu, Ning Zhang
Summary: This paper investigates the stress and displacement of a layered soil with a fractional-order viscoelastic model under time-varying loads. The correctness of the solutions is validated using numerical methods and comparison with existing literature. The research findings are of significant importance for exploring soil behavior and its engineering applications under time-varying loads.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Thuy Dong Dang, Thi Kieu My Do, Minh Duc Vu, Ngoc Ly Le, Tho Hung Vu, Hoai Nam Vu
Summary: This paper investigates the nonlinear torsional buckling of corrugated core sandwich toroidal shell segments with functionally graded graphene-reinforced composite (FG-GRC) laminated coatings in temperature change using the Ritz energy method. The results show the significant beneficial effects of FG-GRC laminated coatings and corrugated core on the nonlinear buckling responses of structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Zhihao Zhai, Chengbiao Cai, Qinglai Zhang, Shengyang Zhu
Summary: This paper investigates the effect of localized cracks induced by environmental factors on the dynamic performance and service life of ballastless track in high-speed railways. A mathematical approach for forced vibrations of Mindlin plates with a side crack is derived and implemented into a train-track coupled dynamic system. The accuracy of this approach is verified by comparing with simulation and experimental results, and the dynamic behavior of the side crack under different conditions is analyzed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
James Vidler, Andrei Kotousov, Ching-Tai Ng
Summary: The far-field methodology, developed by J.C. Maxwell, is utilized to estimate the effective third order elastic constants of composite media containing random distribution of spherical particles. The results agree with previous studies and can be applied to homogenization problems in other fields.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Kim Q. Tran, Tien-Dat Hoang, Jaehong Lee, H. Nguyen-Xuan
Summary: This study presents novel frameworks for graphene platelets reinforced functionally graded triply periodic minimal surface (GPLR-FG-TPMS) plates and investigates their performance through static and free vibration analyses. The results show that the mass density framework has potential for comparing different porous cores and provides a low weight and high stiffness-to-weight ratio. Primitive plates exhibit superior performance among thick plates.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bence Hauck, Andras Szekrenyes
Summary: This study explores several methods for computing the J-integral in laminated composite plate structures with delamination. It introduces two special types of plate finite elements and a numerical algorithm. The study presents compact formulations for calculating the J-integral and applies matrix multiplication to take advantage of plate transition elements. The models and algorithms are applied to case studies and compared with analytical and previously used finite element solutions.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Wu Ce Xing, Jiaxing Wang, Yan Qing Wang
Summary: This paper proposes an effective mathematical model for bolted flange joints to study their vibration characteristics. By modeling the flange and bolted joints, governing equations are derived. Experimental studies confirm that the model can accurately predict the vibration characteristics of multiple-plate structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Pingchao Yu, Li Hou, Ke Jiang, Zihan Jiang, Xuanjun Tao
Summary: This paper investigates the imbalance problem in rotating machinery and finds that mass imbalance can induce lateral-torsional coupling vibration. By developing a model and conducting detailed analysis, it is discovered that mass imbalance leads to nonlinear time-varying characteristics and there is no steady-state torsional vibration in small unbalanced rotors. Under largely unbalanced conditions, both resonant and unstable behavior can be observed, and increasing lateral damping can suppress instability and reduce lateral amplitude in the resonance region.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Yong Cao, Ziwen Guo, Yilin Qu
Summary: This paper investigates the mechanically induced electric potential and charge redistribution in a piezoelectric semiconductor cylindrical shell. The results show that doping levels can affect the electric potentials and mechanical displacements, and alter the peak position of the zeroth-order electric potential. The doping level also has an inhibiting effect on the first natural frequency. These findings are crucial for optimizing the design and performance of cylindrical shell-shaped sensors and energy harvesters.
APPLIED MATHEMATICAL MODELLING
(2024)
