An Efficient Method for Systems of Variable Coefficient Coupled Burgers’ Equation with Time-Fractional Derivative by Hossein Aminikhah, Nasrin Malekzadeh

“…Results indicate that the introduced method is promising for solving other types of systems of nonlinear fractional-order partial differential equations.…”
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Strong Convergence of a New Hybrid Iterative Scheme for Nonexpensive Mappings and Applications by Jie Jia, Khurram Shabbir, Khushdil Ahmad, Nehad Ali Shah, Thongchai Botmart

“…By using the Picard-Thakur hybrid iterative scheme, we can find the solution of delay differential equations and also prove some convergence results for nonexpansive mapping in a uniformly convex Banach space.…”
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Analytic Solutions of Some Self-Adjoint Equations by Using Variable Change Method and Its Applications by Mehdi Delkhosh, Mohammad Delkhosh

“…Many applications of various self-adjoint differential equations, whose solutions are complex, are produced (Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011). …”
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Analysis of the Nonlinear Structural-Acoustic Resonant Frequencies of a Rectangular Tube with a Flexible End Using Harmonic Balance and Homotopy Perturbation Methods by Y. Y. Lee

“…The structural acoustic problem considered in this study is the nonlinear resonant frequencies of a rectangular tube with one open end, one flexible end, and four rigid side walls A multiacoustic single structural modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibration of the flexible end and acoustic pressure induced within the tube. …”
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On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods by A. K. Gupta, S. Saha Ray

“…Haar wavelet method is an efficient numerical method for the numerical solution of arbitrary order partial differential equations like Burgers-Fisher and generalized Fisher equations. …”
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Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations by Azam Zahrani, Mashaallah Matinfar, Mostafa Eslami

“…This work concerns the numerical solutions of a category of nonlinear and linear time-fractional partial differential equations (TFPDEs) that are called time-fractional inhomogeneous KdV and nonlinear time-fractional KdV equations, respectively. …”
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Epidemic Analysis and Mathematical Modelling of Influenza with Vaccination. by Musiime, Catherine

“…In this study, we discuss a SLIRV model developed by Jonnalagadda & Gaddam (2016) for the transmission of influenza A with vaccination using tools from ordinary differential equations. We show that if the product of the recruitment rate and the ratio of infection rate to mean latent period is less than the product the sums µ + m, µ + m and + a + y; where µ, a, y, m and 1/ware natural death rate, disease-related death rate, recovery rate, vaccination rate and mean latent period, respectively; then the disease-free equilibrium will be locally and globally asymptotically stable, an indication that that disease can be eradicated from the population.…”
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Constructions of solitary wave solutions for huge family of NPDEs with three applications. by Hanan A Alkhidhr, Y Omar

“…This study offers closed-form solutions for the frequently utilised families of nonlinear partial differential equations (NPDEs). This form based on the He's semi-inverse technique. …”
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An Algorithm for Higher Order Hopf Normal Forms by A.Y.T. Leung, T. Ge

“…This article provides an explicit formula for the normalization of nonlinear differential equations. The higher order normal form is given explicitly. …”
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Mathematical Modeling for Optimal Management of Human Resources in Banking Sector of Bangladesh by Uzzwal Kumar Mallick, Md. Haider Ali Biswas

“…A system of ordinary nonlinear differential equations has three state variables including vacancies. …”
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Chaotic Convection in a Viscoelastic Fluid Saturated Porous Medium with a Heat Source by B. S. Bhadauria

“…An autonomous system of fourth-order differential equations has been deduced by using a truncated Fourier series. …”
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Weyl-Euler-Lagrange Equations of Motion on Flat Manifold by Zeki Kasap

“…In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. …”
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Contrast Expansion Method for Elastic Incompressible Fibrous Composites by Piotr Drygaś, Vladimir Mityushev

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Elastic Equilibrium of Porous Cosserat Media with Double Porosity by Roman Janjgava

“…The corresponding three-dimensional system of differential equations is derived. Detailed consideration is given to the case of plane deformation. …”
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An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations by Hooman Darvishi, M. T. Darvishi

“…These algorithms are applied for solving two real stiff systems of ordinary differential equations. These systems arise from an HIV spreading model and an SIR model of an epidemic which formulates the spread of a nonfatal disease in a certain population. …”
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Heat transportation of 3D chemically reactive flow of Jeffrey nanofluid over a porous frame with variable thermal conductivity by Nahid Fatima, Aaqib Majeed, Taoufik Saidani, Nouman Ijaz, Kamal Barghout, Nidal Abu-Libdeh

“…To model these phenomena, we employ the boundary layer approximation to derive a system of partial differential equations (PDEs). These PDEs are subsequently simplified into more manageable ordinary differential equations (ODEs) using the similarity variables. …”
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Heteroclinic bifurcation for a general predator-prey model with Allee effect and state feedback impulsive control strategy by Qizhen Xiao, Binxiang Dai

“…We firstly show the existence of order-$1$ heteroclinic cycle and order-$1$ positive periodic solutions by using the geometric theory of differential equations for the unperturbed system. Based on the theory of rotated vector fields, the order-$1$ positive periodic solutions and heteroclinic bifurcation are studied for the perturbed system. …”
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Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions by Yan Gao, Songlin Liu

“…In addition, a fine description of the sixth-order CFD schemes is also developed for equations with constant coefficients, which is used to discuss certain partial differential equations (PDEs) with arbitrary dimensions. In this paper, various ways of numerical test calculations are prepared to evaluate performance of the fourth-order CFD and sixth-order CFD schemes, respectively, and the empirical results are proved to verify the effectiveness of the schemes in this paper.…”
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Soret and Dufour Effects on Natural Convection Flow Past a Vertical Surface in a Porous Medium with Variable Viscosity by M. B. K. Moorthy, K. Senthilvadivu

“…The governing equations of continuity, momentum, energy, and concentrations are transformed into nonlinear ordinary differential equations, using similarity transformations, and then solved by using Runge-Kutta-Gill method along with shooting technique. …”
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Analysis of electroelastic frictionless contact problems with adhesion by Mircea Sofonea, Rachid Arhab, Raafat Tarraf

“…The proofs are based on arguments of time-dependent variational inequalities, differential equations, and fixed point. Moreover, we prove that the solution of the Signorini contact problem can be obtained as the limit of the solution of the contact problem with normal compliance as the stiffness coefficient of the foundation converges to infinity.…”
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