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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Vibration Optimization of Multi-gear Transmission System based on Mixed-discrete Method by Zhang Lijuan

“…Taking the gear pair meshing stiffness,meshing damping and transmission error into consideration,the six degree of freedom pure torsion model differential equation of multi- gear transmission is set up based on lumped parameter method,the vibration accelerated speed of each component is obtained by adopting harmonic balance method. …”
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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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NONLINEAR PRIMARY RESONANCE OF A CIRCULAR SANDWICH PLATE UNDER STATIC LOAD by GUO Wei, DU GuoJun, HU YuDa

“…The axisymmetric nonlinear vibration differential equation of the plate under static load is obtained by Galerkin method. …”
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Dynamics Characteristic Analysis of a Spur Gear based on Measured Tooth Surface Error by Chen Siyu, Bai Fan, Tang Jinyuan

“…In order to study the influence of tooth surface error on gear system,the static transmission error is calculated for gear system with measured errors such as profile deviation,run out and pitch errors by tooth contact analysis method.In this work,a differential equation of vibration for gear system with time-varying meshing stiffness,blackness,meshing damping and static transmission error is established on the basis of previous research for gear transmission system. …”
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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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The discontinuous solutions of Lame’s equations for a conical defect by Natalya D. Vaysfel'd, O. Reut

“…A discontinuous solution of a certain differential equation in the partial derivatives is a solution that satisfies this equation throughout the region of determining an unknown function, with the exception of the defect points. …”
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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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DYNAMIC CHARACTERISTICS ANALYSIS OF SPHERICAL HYBRID SLIDING BEARINGS by JI DongSheng, SHEN JingFeng, CHEN YuFei, ZHOU YiHao

“…Taking spherical hybrid sliding bearings as the research object, established the mathematical model of lubrication analysis of spherical sliding bearings, the dynamic liquid lubrication equation under laminar flow was derived by the perturbation method, the partial differential equation of disturbance pressure was solved by the finite difference method, and the liquid was calculated numerically. …”
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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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MAGNETOELASTIC NATURAL VIBRATION OF CONDUCTIVE CIRCULAR PLATE IN CURRENT-CARRYING COILS by XU HaoRan, HU YuDa, LI WenPing

“…By setting of a displacement function and using of Galerkin method,the magnetoelastic axisymmetric vibration differential equation of the plate and the expression of the natural frequency were obtained. …”
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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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