Article
Mathematics, Interdisciplinary Applications
Halil Anac
Summary: In this paper, the nonlinear system of local fractional partial differential equations is solved using the local fractional Elzaki transform decomposition method, which combines the local fractional Elzaki transform and the Adomian decomposition method. Applications related to this system are presented.
FRACTAL AND FRACTIONAL
(2022)
Article
Physics, Applied
Dianchen Lu, Muhammad Suleman, Muhammad Ramzan, Jamshaid Ul Rahman
Summary: In this paper, the Fractional Elzaki Projected Differential Transform Method (FEPDTM) is applied to develop new efficient approximate solutions of coupled nonlinear fractional KdV equations. The method demonstrates realistic reliance on fractional-order values and proves to be more efficient than known analytical and computational methods, showing reduced computational time.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2021)
Article
Mathematics, Applied
M. S. Alqurashi, Saima Rashid, Bushra Kanwal, Fahd Jarad, S. K. Elagan
Summary: This article introduces the broadening description of Caputo fractional derivatives and constructs a novel decomposition method for solving nonlinear fuzzy fractional partial differential equations using the fuzzy Elzaki transform. The correctness and capabilities of the proposed algorithm are demonstrated through experiments. The article discusses future research directions.
Article
Multidisciplinary Sciences
Abdul Hamid Ganie, Mashael M. AlBaidani, Adnan Khan
Summary: Compared to fractional-order differential equations, integer-order differential equations fail to explain various phenomena effectively in science and engineering. This article employs efficient analytical techniques utilizing the Caputo operator to investigate the solutions of fractional partial differential equations. The Adomian decomposition method, homotopy perturbation method, and Elzaki transformation are utilized to compute comprehensive results for the specified problems. The methods employed are simple, efficient, and provide a series-form solution with easily computable components and a higher convergence rate to the precise solution of the targeted problems. Graphs in two and three dimensions are used to visualize the solutions of the proposed fractional models. The results of this study serve as a valuable tool for solving fractional partial differential equations.
Article
Mathematics
Gbenga O. Ojo, Nazim I. Mahmudov
Summary: This paper presents a new approximate analytical method for solving the fractional biological population model, based on the Aboodh transform method and a new iterative method. Illustrative cases are considered for comparison between exact and numerical solutions for different values of alpha, with surface plots provided to understand the effect of the fractional order. The method is efficient, accurate, and easy to implement with less computational effort.
Article
Mathematics
Mawia Osman, Yonghui Xia, Omer Abdalrhman Omer, Ahmed Hamoud
Summary: In this article, the fuzzy Adomian decomposition method and fuzzy modified Laplace decomposition method are presented to solve the fuzzy fractional Navier-Stokes equations. The fuzzy Elzaki transform and fuzzy Elzaki decomposition method are also investigated for solving fuzzy linear-nonlinear Schrodinger differential equations. Comparisons are made with other methods, and the proposed methods are found to be simpler and consistent with analytical and numerical results.
Article
Mathematics, Applied
KangLe Wang
Summary: This study proposes a fractal vibration model to investigate the effect of microgravity on vibration properties, utilizing fractal derivative, He's frequency formula, and fractal semi-inverse method to establish the model and obtain frequency. The research demonstrates that the method is simple, efficient, and precise, clarifying the relationship between frequency and amplitude, and discussing the impact of microgravity conditions on vibration properties.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Physics, Multidisciplinary
Arshad Hussain, Sayed Saifullah, Amir Ali
Summary: This article discusses the theory, properties, and applications of a novel integral transform called the J-transform (JT) for fractional differential equations. The author presents several fundamental theorems on fractional Riemann-Liouville and Caputo derivatives and proves important results and functions using the proposed transform. The exact and approximate solutions to various fractional differential equations are provided, demonstrating the validity, accuracy, and efficiency of this fast-converging transform. It is observed that the JT is a functional and valuable method for studying nonlinear problems in science and engineering.
Article
Mathematics
Meshari Alesemi
Summary: This research presents a combined approach utilizing an Elzaki transform, the homotopy perturbation method, and the Adomian decomposition method to solve nonlinear fractional shock wave equations. The nonlinear equation is transformed into an integral equation using the Elzaki transform, and then approximated using the homotopy perturbation method and Adomian decomposition method. The proposed method is evaluated through numerical experiments and compared with existing methods, demonstrating its accuracy and efficiency in solving nonlinear fractional shock wave equations.
Article
Mathematics, Applied
Zhonghua Qiao, Xuguang Yang, Yuze Zhang
Summary: A novel lattice Boltzmann equation model is proposed to solve fourth order NPDE, featuring a source distribution function to eliminate unwanted terms. Through numerical experiments, it is shown that the performance of this model is superior to existing ones.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Engineering, Electrical & Electronic
Sandeep Malik, Mir Sajjad Hashemi, Sachin Kumar, Hadi Rezazadeh, W. Mahmoud, M. S. Osman
Summary: The purpose of this work is to find innovative exact solutions for nonlinear partial differential equations using the new Kudryashov approach. The technique provides novel exact solutions of soliton types. 3D and 2D plots of higher dimensional Klein-Gordon, Kadomtsev-Petviashvili, and Boussinesq equations are shown to better understand the nonlinear wave structures. The new Kudryashov technique is effective and simple, providing new generalized solitonic wave profiles that enhance the understanding of the development and dynamic nature of such models.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Materials Science, Multidisciplinary
Hijaz Ahmad, Tufail A. Khan, Predrag S. Stanimirovic, Wasfi Shatanawi, Thongchai Botmart
Summary: This study investigates the modified variational iteration algorithm-I, which is used for solving different types of nonlinear partial differential equations in modeling physical phenomena. The algorithm incorporates a supplementary parameter to ensure faster convergence. The results obtained from this algorithm are compared with exact and numerical solutions produced by various methods, demonstrating its efficiency, precision, and applicability. The proposed algorithm is highly valuable for solving practical problems in fields of applied physical sciences and engineering.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Mostafa M. A. Khater
Summary: This research paper presents precise solutions for nonlinear fractional population biology (FBP) models using the generalized Khater (GK) technique and Atangana's conformable fractional (ACF) derivative operator. Various mathematical explanations and graphical representations are employed to enhance the understanding of these methods. The effectiveness and accuracy of the employed analytical and numerical techniques are verified through validation tests.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Marc Jornet
Summary: In this paper, the uncertainty propagation of Burgers' equation with random initial condition and viscosity is quantified using the differential transform method. Convergence of the inverse differential transform is shown to only be expected in a small neighborhood in space-time when the input random parameters have small dispersion. Rapid approximations of main statistics and density function can be determined at virtually no computational cost in the region of convergence.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics, Applied
A. Ghose-Choudhury, Sudip Garai
Summary: This article discusses the use of a comparison method to obtain exact solutions for nonlinear partial differential equations (PDEs) through their traveling wave reductions. The method, proposed by N. A. Kudryashov, is extended to include solutions expressed in terms of both the logistic function and the tanh$$ \tanh $$-class of functions. The article derives the standard set of second-order ordinary differential equations (ODEs) that have the logistic and tanh$$ \tanh $$ functions as solutions and also extends the analysis to third-order cases.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(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
Physics, Applied
Muhammad Ramzan, Jawad Ali, Nazia Shahmir, Hassan Ali S. Ghazwani, Kottakkaran Sooppy Nisar, C. Ahamed Saleel
Summary: This study numerically solves a set of ordinary differential equations to analyze the influence of a magnetic dipole on the flow of non-electrical conducting Oldroyd-B fluid. The effects of thermophoretic particle deposition and chemical reaction parameter on velocity, temperature, and concentration are examined. The model is validated in the limiting case.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Applied
Muhammad Ramzan, Naila Shaheen, Hassan Ali S. Ghazwani, Kottakkaran Sooppy Nisar, C. Ahamed Saleel
Summary: This paper studies the flow of a chemical reactive Maxwell nanofluid in porous media, considering the temperature-dependent thermal conductivity and spinning cone conditions. The effects of various parameters on velocity, heat, and mass transfers are analyzed using numerical solutions and graphical representation.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Applied
Jamshaid Ul Rahman, Abdul Mannan, Mohamed E. Ghoneim, Mansour F. Yassen, Jamil Abbas Haider
Summary: This study examines the solutions to nonlinear partial differential equations and ordinary differential equations. Currently, there are no well-known methods for solving nonlinear equations, but different problems can be solved using different approaches like the variation method. In this paper, a new method called the variation iterative method with Laplace transformation is used to find a solution for a highly nonlinear evolution of a simple pendulum.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Applied
Muhammad Ramzan, Hina Gul, Hassan Ali S. Ghazwani, Kottakkaran Sooppy Nisar, Mohamed Abbas, C. Ahamed Saleel
Summary: Hybrid nanofluids (HNFs) are a new type of nanofluids with a wide range of applications. The behavior of Hamilton-Crosser (H-C) and Yamada-Ota (Y-O) HNF flow models past a stretching cylinder is explored in this study. The results show that the Y-O HNF flow model performs better and blade-shaped nanoparticles have a higher heat transfer rate.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Applied
Muhammad Ramzan, Hina Gul, Hassan Ali S. Ghazwani, Kottakkaran Sooppy Nisar, C. Ahamed Saleel
Summary: This study investigates the flow model of hybrid nanofluids (gold-silver/engine oil) over a stretched cylindrical surface and a sheet in a permeable medium. The novelty lies in considering surface-catalyzed reaction and homogeneous-heterogeneous reactions to accelerate chemical reactions. The heat transport phenomena are enhanced with the support of Joule heating, heat absorption/generation, and the convective heat boundary condition. Ordinary differential equations are obtained using boundary layer theory and numerically solved using the Keller box method. The results show that the thermal profile enhances while the velocity field reduces for different magnetic parameter estimates, and the fluid concentration decreases when the surface-catalyzed parameter increases.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Applied
Muhammad Ramzan, Naila Shaheen, Hassan Ali S. Ghazwani, Kottakkaran Sooppy Nisar, C. Ahamed Saleel
Summary: In this study, temperature-dependent Yamada-Ota and Xue hybrid nanoliquid models were used to investigate the thermal performance over a curved stretchable surface embedded in an absorbent media. The results showed that the modified Fourier law combined with temperature-dependent thermal conductivity, Newtonian heating, and variable heat source/sink can enhance the thermal performance. Additionally, it was observed that the fluid velocity decreases with an increase in the velocity slip parameter and increases with an increase in the curvature parameter. Moreover, the temperature field is enhanced with the conjugate parameter. The results are in good agreement with the existing literature.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Correction
Computer Science, Information Systems
Akhtar Ali, Majid Hussain, Zafar Ali, Jamshaid Ul Rahman, Muhammad Hussan
Article
Engineering, Multidisciplinary
Mumtaz Khan, Dianchen Lu
Summary: This article numerically investigates the time-dependent fractional non-Newtonian fluid model on a vertical plane in a Darcy medium. A generalized Scott-Bliar model is employed to control the flow and mass transfer in the boundary layer region. The analysis shows that the fractional exponent significantly affects the concentration of chemical species and provides insights into the chemical process in the fractional Casson fluid model.
AIN SHAMS ENGINEERING JOURNAL
(2023)
Article
Thermodynamics
Umair Rashid, Hasan Shahzad, Dianchen Lu, Xinhua Wang, Afraz Hussain Majeed
Summary: The mathematical analysis of fluid flow in a wavy cavity with a heated circular center is investigated in this study. The focus is on the mass and heat transfer in MHD Casson fluid flow. The results show that the rate of heat transfer increases while the rate of mass transfer decreases with the increasing Casson parameter.
CASE STUDIES IN THERMAL ENGINEERING
(2023)
Article
Physics, Applied
Jamshaid Ul Rahman, Faiza Makhdoom, Akhtar Ali, Sana Danish
Summary: Many real-life problems can be modeled as differential equations, and there are various methods proposed for their solution. However, some limitations may be encountered. Artificial neural networks, being theoretically strong and computationally favorable, can be used to approximate the solutions of these differential equations. In this study, mathematical models for biophysics systems were developed based on their dynamical behavior, and a neural network with a single hidden layer of 50 neurons and the Broyden-Fletcher-Goldfarb-Shanno algorithm were employed to simulate the results for a population of micro-organisms. The results obtained from the neural network were compared with those from analytic methods, and similar results were observed.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Thermodynamics
Umair Rashid, Dianchen Lu, Quaid Iqbal
Summary: The study investigates the influence of nanoparticle shape on the flow and heat conduction of nanofluid in a cavity. The flow behavior and heat transfer of spherical, columnar, and lamina-shaped nanoparticles in the cavity are simulated using the finite element method. The results show that the lamina-shaped nanoparticles perform better in temperature distribution and heat transfer of the nanofluid.
CASE STUDIES IN THERMAL ENGINEERING
(2023)
Article
Mathematics
Jamshaid Ul Rahman, Sana Danish, Dianchen Lu
Summary: In this paper, a novel deep neural network-based method is proposed to simulate the Sel'kov glycolysis model, which overcomes the limitations of conventional numerical methods and offers greater reliability for nonlinear dynamics. The results demonstrate that the proposed approach outperforms traditional methods, providing researchers with deeper insights into the complex interactions that drive biochemical systems.
Article
Thermodynamics
Umair Rashid, Naeem Ullah, Dianchen Lu, Hamiden Abd El-Wahed Khalifa
Summary: The study investigates the heat transfer characteristics and energy transfer of power law fluid flow in a crown cavity with an adjustable heated cylinder. The results indicate that the kinetic energy and Nusselt number are higher for shear thinning, while they are lower for shear thickening.
CASE STUDIES IN THERMAL ENGINEERING
(2023)
Article
Engineering, Mechanical
Jamil A. A. Haider, Sana Gul, Jamshaid U. U. Rahman, Fiazud D. D. Zaman
Summary: This article focuses on the exact periodic solutions of nonlinear wave equations using the well-known Jacobi elliptic function expansion method, which is more general than the hyperbolic tangent function expansion method. The periodic solutions that contain both solitary wave and shock wave solutions are found using this method. The new results are computed using the closed-form solution, including solitary or shock wave solutions obtained using the Jacobi elliptic function method. The corresponding solitary or shock wave solutions are compared with the actual results. The results are visualised, and the periodic behaviour of the solution is described in detail. It is found that shock waves break with time, while solitary waves continuously improve with time.
ACTA MECHANICA ET AUTOMATICA
(2023)
