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Article
Engineering, Multidisciplinary
Mubashir Qayyum et al.
Summary: In this paper, an extended residual power series method (RPSM) is proposed to solve ordinary differential equations with boundary conditions. The reliability of the proposed methodology is tested by comparing the results with other schemes for different boundary value problems (BVPs). The analysis shows that the extended approach can handle BVPs easily and provide a convergent series solution without the need for discretization, perturbation, or linearization. Therefore, RPSM is a better choice for scientists and researchers working in various fields of engineering and sciences.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Physics, Multidisciplinary
Farnaz Ismail et al.
Summary: This article presents a fractional analysis of steady flow of magneto-hydrodynamic fluid with variable viscosity and thermal conductivity on permeable stretched surface. The obtained nonlinear coupled fractional differential equations are solved using fractional calculus and the homotopy perturbation method. The study investigates the impact of various parameters on velocity and temperature profiles and provides key observations related to these effects.
WAVES IN RANDOM AND COMPLEX MEDIA
(2022)
Article
Engineering, Multidisciplinary
Amjad Shaikh et al.
Summary: This paper presents and investigates a mathematical model describing the HIV/AIDS transmission dynamics in the presence of an aware community using a specific fractional differential operator. The existence and uniqueness conditions of the model are obtained through the fixed point theorem, and an approximate solution is obtained using the iterative Laplace transform approach. The necessary conditions for disease control and numerical simulations for different fractional orders are explored, along with a comparison between numerical results obtained using different operators.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Mubashir Qayyum et al.
Summary: In this research, the He-Laplace algorithm is extended to generalized third order, time-fractional, Korteweg-de Vries (KdV) models. The convergence and error estimation of the algorithm are confirmed theoretically and numerically, with numerical convergence and error analysis performed by computing residual errors. Graphical illustrations demonstrate the effect of the fractional parameter on the solution.
Article
Astronomy & Astrophysics
Mubashir Qayyum et al.
Summary: This paper proposes a new approach to predict and analyze nonlinear time-fractional coupled KdV systems, providing a convergent series solution by applying simple steps and symbolic computations. Numerical simulations demonstrate the superiority of this method in terms of accuracy and computational efficiency.
Article
Astronomy & Astrophysics
Mubashir Qayyum et al.
Summary: This research proposes a new methodology to observe a class of time-fractional generalized fifth-order Korteweg-de Vries equations and applies it to several related models. The method provides improved and convergent series solutions through symbolic computation. The results show that this method outperforms other fractional KdV schemes in terms of accuracy and computational complexity.
Article
Mathematics, Interdisciplinary Applications
Kottakkaran Sooppy Nisar et al.
Summary: This article examines the effect of the yellow virus on Capsicum annuum (C. annuum) through whiteflies (Bemisia tabaci) using a fractional model. The model is analyzed through equilibrium points, reproductive number, and local and global stability. The study discusses optimal control methods using the Atangana-Baleanu derivative and Verticillium lecanii (V. lecanii) to reduce the spread of the virus. Numerical results demonstrate that using 60% of V. lecanii can control the spread of the yellow virus in infected whiteflies and C. annuum within 10 days.
FRACTAL AND FRACTIONAL
(2022)
Article
Automation & Control Systems
V. Vijayakumar et al.
Summary: In this manuscript, a group of sufficient conditions for approximate controllability of second order nonlocal neutral differential evolution inclusions is organized. These conditions are further developed to analyze the approximate controllability of impulsive systems. Lastly, a model is presented to illustrate the theory.
IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION
(2021)
Article
Mathematics, Applied
Behzad Ghanbari
Summary: This paper presents a new efficient technique for retrieving exact fractional solutions to local fractional Gardner's equation defined on Cantor sets, using numerical simulations to demonstrate the dynamic behavior of the results. The method is simple, efficient, accurate, and free of errors in both application and calculation, making it suitable for handling other partial differential equations involving local fractional derivatives.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Engineering, Multidisciplinary
Mostafa M. A. Khater et al.
Summary: This research focuses on studying the computational solutions of the modified BBM equation using the modified Khater method, investigating the stability property of the obtained solutions, and evaluating the initial and boundary conditions to find numerical solutions of the suggested model using B-spline collection schemes. The model describes the propagation of long waves in nonlinear dispersive media in optical illusions field, with four distinct types of sketches employed for better understanding the obtained solutions.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Physics, Applied
Mostafa M. A. Khater et al.
Summary: This paper investigates the accuracy of stable analytical solutions for the nonlinear fractional nonlinear time-space telegraph equation using the trigonometric-quantic-B-spline method. The study focuses on obtaining initial and boundary conditions from the analytical solutions to facilitate the application of the numerical scheme. Additionally, the accuracy of the analytical solutions is examined through the properties of the Hamiltonian system.
MODERN PHYSICS LETTERS B
(2021)
Article
Physics, Multidisciplinary
Mostafa M. A. Khater et al.
Summary: This paper investigates the analytical and semi-analytical solutions of the generalized CBS equation, demonstrating the dynamic behavior of soliton wave solutions in plasma. The method used shows effectiveness in various nonlinear evolution equations.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2021)
Article
Physics, Applied
Mostafa M. A. Khater
Summary: The research paper employs the trigonometric quintic B-spline scheme to investigate the numerical solution of Zakharov's nonlinear dimensional equation, exploring the connection between high-frequency Langmuir and low-frequency ion-acoustic waves with various applications. Different computational schemes have been utilized to study the model's moving wave solution, with innovative solutions established to determine suitable conditions for implementing multiple numerical schemes. The precision of the collected analytical solutions is analyzed using the trigonometric quintic B-spline method, and distinct drawings are provided to illustrate the accuracy of the numerical and computational solutions.
MODERN PHYSICS LETTERS B
(2021)
Article
Physics, Applied
Mostafa M. A. Khater
Summary: This paper examines three different recent computational schemes for obtaining novel solitary wave solutions of cubic-quintic nonlinear Helmholtz model, where various types of wave solutions are explained and described in precise sketches. The methods' performance is explained to demonstrate their effectiveness and power.
MODERN PHYSICS LETTERS B
(2021)
Article
Multidisciplinary Sciences
Wu Li et al.
Summary: In this article, numerous wave solutions of the (2 + 1)-dimensional KP-BBM model are constructed using the MDA and MK methods, which are based on symmetry. These solutions are explained through 3D, 2D, and contour sketches, and their accuracy is tested by comparing with numerical results. The synchronization between computational and numerical solutions is shown through two-dimensional and distribution plots.
Article
Computer Science, Information Systems
Olumuyiwa J. Peter et al.
Summary: A mathematical model was proposed to investigate the transmission and control mechanisms of COVID-19 in the community of Nigeria, using stability theory of differential equations. The study examined the qualitative behavior of the model and determined stability conditions for disease-free and pandemic equilibrium. Through numerical simulations and theoretical analysis, the impacts of various biological parameters on transmission dynamics were explored to identify significant strategies for disease control.
CMC-COMPUTERS MATERIALS & CONTINUA
(2021)
Article
Physics, Multidisciplinary
Tariq Abbas et al.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2020)
Article
Engineering, Multidisciplinary
Kolade M. Owolabi et al.
ALEXANDRIA ENGINEERING JOURNAL
(2020)
Article
Mathematics, Applied
Kumararaju Logeswari et al.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2020)
Article
Engineering, Aerospace
Inayat Ullah et al.
PROPULSION AND POWER RESEARCH
(2019)
Article
Automation & Control Systems
V. Vijayakumar
IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION
(2018)
Article
Mathematics, Applied
V. Vijayakumar et al.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2017)
Article
Mathematics, Applied
Ahmad El-Ajou et al.
APPLIED MATHEMATICS AND COMPUTATION
(2015)
Article
Computer Science, Interdisciplinary Applications
Ahmad El-Ajou et al.
JOURNAL OF COMPUTATIONAL PHYSICS
(2015)
Article
Mathematics, Applied
Omar Abu Arqub et al.
ABSTRACT AND APPLIED ANALYSIS
(2013)
Article
Mathematics, Interdisciplinary Applications
Omar Abu Arqub et al.
DISCRETE DYNAMICS IN NATURE AND SOCIETY
(2013)
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Mathematics, Applied
Muhammad Aslam Noor et al.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2009)
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Chemistry, Physical
Mehdi Dehghan et al.
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES
(2009)
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J. Biazar et al.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2007)
