Lyapunov Stability of the Generalized Stochastic Pantograph Equation by Ramazan Kadiev, Arcady Ponosov

“…The framework can be applied to any stochastic functional differential equation with finite dimensional initial conditions.…”
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Bifurcation Type Change of AC Electrostatically Actuated MEMS Resonators due to DC Bias by Dumitru I. Caruntu, Kyle N. Taylor

“…The method of multiple scales (MMS) is used to solve the dimensionless differential equation of motion of the resonator and find the steady-state solutions. …”
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A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel by Shabir Ahmad, Aman Ullah, Ali Akgül, Manuel De la Sen

“…We derive an algorithm for the solution of Caputo-Fabrizio (CF) fractional order partial differential equation in series form and show its convergence to the exact solution. …”
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Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising by V. B. Surya Prasath, Arindama Singh

“…We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of anisotropic diffusion. …”
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Orthogonal Polynomials on Radial Rays in the Complex Plane: Construction, Properties and Applications by Gradimir V. Milovanović

“…Recurrence relations for such kinds of orthogonal polynomials and their zero distribution, as well as a connection with the standard polynomials orthogonal on the real line, are derived, including the corresponding linear differential equation of the second order. Finally, some applications in physics and electrostatics are mentioned.…”
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Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation by Naveed Iqbal, Azmat Ullah Khan Niazi, Ramsha Shafqat, Shamsullah Zaland

“…With the help of few conditions on functions P:I×E1×E1⟶E1, WI is control and it belongs to E1, A∈FI,LE1, and α stands for the highly continuous fuzzy differential equation generator. Finally, a few instances of fuzzy fractional differential equations are shown.…”
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Mathematical Model and Solution for Fingering Phenomenon in Double Phase Flow through Homogeneous Porous Media by Piyush R. Mistry, Vikas H. Pradhan, Khyati R. Desai

“…An approximate analytical solution of the governing nonlinear partial differential equation is obtained using variational iteration method with the use of Mathematica software.…”
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Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings by Xinlei Yi, Wenlian Lu, Tianping Chen

“…We study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). Here, the coupling is timevarying in both network structure and reaction dynamics. …”
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Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme by Dagnachew Mengstie Tefera, Awoke Andargie Tiruneh, Getachew Adamu Derese

“…This paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. …”
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New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds by W. M. Abd-Elhameed, E. H. Doha, Y. H. Youssri

“…The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spectral collocation method to transform the differential equation with its boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients which can be efficiently solved. …”
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An Extended Newmark-FDTD Method for Complex Dispersive Media by Yu-Qiang Zhang, Peng-Ju Yang

“…In this paper, the time-stepping equation of the polarization vector is derived by applying simultaneously the Newmark algorithm to the two sides of a second-order time-domain differential equation obtained from the relation between the polarization vector and electric field intensity in the frequency domain by the inverse Fourier transform. …”
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On the Korteweg-de Vries equation: an associated equation by Eugene P. Schlereth, Ervin Y. Rodin

“…The purpose of this paper is to describe a relationship between the Korteweg-de Vries (KdV) equation ut−6uux+uxxx=0and another nonlinear partial differential equation of the form zt+zxxx−3zxzxxz=H(t)z.The second equation will be called the Associated Equation (AE) and the connection between the two will be explained. …”
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Comparison of Different Analytic Solutions to Axisymmetric Squeezing Fluid Flow between Two Infinite Parallel Plates with Slip Boundary Conditions by Hamid Khan, S. Islam, Javed Ali, Inayat Ali Shah

“…We investigate squeezing flow between two large parallel plates by transforming the basic governing equations of the first grade fluid to an ordinary nonlinear differential equation using the stream functions ur(r,z,t)=(1/r)(∂ψ/∂z) and uz(r,z,t)=−(1/r)(∂ψ/∂r) and a transformation ψ(r,z)=r2F(z). …”
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Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient by Te-Wen Tu, Sen-Yung Lee

“…By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. …”
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Effects of Thermal Radiation on Mixed Convection Flow of a Micropolar Fluid from an Unsteady Stretching Surface with Viscous Dissipation and Heat Generation/Absorption by Khilap Singh, Manoj Kumar

“…The model contains nonlinear coupled partial differential equations which have been converted into ordinary differential equation by using the similarity transformations. …”
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Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments by Wei Li, Chang-Yuan Chen, Shi-Hai Dong

“…We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. …”
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An Improved C-V Model and Application to the Coal Rock Mesocrack Images by Yulong Chen, Hongwei Zhang

“…In order to accurately and comprehensively obtain information about coal rock mesocrack images, image processing technique based on partial differential equation (PDE) is introduced in order to expound on the active contour model without edges and overcome the deficiency of the C-V model. …”
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Importance of Activation Energy on Magnetized Dissipative Casson-Maxwell Fluid through Porous Medium Incorporating Chemical Reaction, Joule Heating, and Soret Effects: Numerical St... by Nesreen Althobaiti

“…The method transforms partial differential equations originating in fluidic systems into nonlinear differential equation systems with the proper degree of similarity which is subsequently resolved utilizing the Lobatto IIIA technique’s powerful computing capabilities. …”
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Time Series Prediction Based on Complex-Valued S-System Model by Bin Yang, Wenzheng Bao, Yuehui Chen

“…The experiment results show that the predicted data are very close to the target ones and our method could obtain the better RMSE, MAP, MAPE, POCID, R2, and ARV performances than ARIMA, radial basis function neural network (RBFNN), flexible neural tree (FNT), ordinary differential equation (ODE), and S-system.…”
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Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous Dissipation by Javad Alinejad, Sina Samarbakhsh

“…The similarity transformation reduces the time-independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations. The obtained equations, including nonlinear equation for the velocity field 𝑓 and differential equation by variable coefficient for the temperature field 𝜃, are solved numerically by using the fourth order of Runge-Kutta integration scheme accompanied by shooting technique with Newton-Raphson iteration method. …”
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