On Integral Transforms and Matrix Functions by Hassan Eltayeb, Adem Kılıçman, Ravi P. Agarwal

“…These transforms are then used to solve the differential equation of a general linear conservative vibration system, a vibrating system with a special type of viscous damping.…”
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Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution by H. Panahi, M. Baradaran

“…We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2). …”
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Pricing Parisian Option under a Stochastic Volatility Model by Min-Ku Lee, Kyu-Hwan Jang

“…A stochastic volatility correction to the Black-Scholes price of the Parisian option is obtained in a partial differential equation form and the solution is characterized numerically.…”
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Vaclovas Bliznikas (1930–1997) – creator of Lithuanian geometers' school by Juozas Banionis

“…The main academic research activity embraced trends of modern geometry, theory of geometrical objects, geometry of differential equation, theory of non-holonomicity ma­nifolds, geometry of supporting elements. …”
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Permanence, Extinction, and Almost Periodic Solution of a Nicholson's Blowflies Model with Feedback Control and Time Delay by Haihui Wu, Shengbin Yu

“…By applying the comparison theorem of the differential equation and fluctuation lemma and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence, extinction, and existence of a unique globally attractive positive almost periodic solution of the system are obtained. …”
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Wavelet-Galerkin Quasilinearization Method for Nonlinear Boundary Value Problems by Umer Saeed, Mujeeb ur Rehman

“…Quasilinearization technique is applied to linearize the nonlinear differential equation and then wavelet-Galerkin method is implemented to linearized differential equations. …”
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Integral price formulas for lookback options by Chenglong Xu, Yue Kuen Kwok

“…The intricacies in the derivation procedures using the partial differential equation techniques stem from the degenerate nature of the pricing models, where the lookback state variables appear only in the auxiliary conditions but not in the governing differential equations. …”
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The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method by Yousef Alnafisah

“…In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two-dimensional stochastic differential equation (SDE) using Matlab program. Our numerical experiments use Matlab to show how our truncation of Itô’-Taylor expansion at an appropriate point produces Milstein method for the SDE.…”
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On nth-order differential operators with Bohr-Neugebauer type property by Aribindi Satyanarayan Rao

“…If the differential operator dndtn−B has a Bohr-Neugebauer type property for Bochner almost periodic functions, then, for any Stepanov almost periodic continuous function g(t) and any Stepanov-bounded solution of the differential equation dndtnu(t)−Bu(t)=g(t), u(n−1),…,u′,u are all almost periodic.…”
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Analytical Solution to 1D Compressible Navier-Stokes Equations by Changsheng Dou, Zishu Zhao

“…We find an interesting phenomenon on the solution to 1D compressible isentropic Navier-Stokes equations with constant viscosity coefficient on x,t∈0,+∞×R+, that is, the solutions to the initial boundary value problem to 1D compressible Navier-Stokes equations in half space can be transformed to the solution to the Riccati differential equation under some suitable conditions.…”
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Exponential Stability of Periodic Solutions for Inertial Type BAM Cohen-Grossberg Neural Networks by Chunfang Miao, Yunquan Ke

“…First, by properly choosing variable substitution, the system is transformed to first order differential equation. Second, some sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov functional and using differential mean value theorem and inequality technique. …”
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Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity by Yongqing Wang, Lishan Liu, Yonghong Wu

“…We discuss the existence of positive solutions of a boundary value problem of nonlinear fractional differential equation with changing sign nonlinearity. We first derive some properties of the associated Green function and then obtain some results on the existence of positive solutions by means of the Krasnoselskii's fixed point theorem in a cone.…”
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Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization by Lei Hu

“…The Hamilton–Jacobi–Bellman equation formulated from the optimal investment problem is a high-dimensional nonlinear partial differential equation and difficult to find its analytical or numerical solutions. …”
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Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation by Robert Willie

“…In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second-order ordinary differential equation. In the semilinear case, under suitable dissipative assumptions on the nonlinear term, we prove the existence of a global attractor for fixed diffusion and that the limiting attractor for large diffusion is finite dimensional.…”
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A Novel Analytical Technique to Obtain Kink Solutions for Higher Order Nonlinear Fractional Evolution Equations by Qazi Mahmood Ul Hassan, Jamshad Ahmad, Muhammad Shakeel

“…A generalized fractional complex transform is appropriately used to convert this equation to ordinary differential equation which subsequently resulted in a number of exact solutions.…”
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Sensitivity Analysis of a Physiochemical Interaction Model Undergoing Changes in the Initial Condition and Duration of Experiment Time by EN Ekaka-a, EO Chukwuocha, NM Nafo

“…The mathematical modelling of physiochemical interactions in the framework of industrial and environmental physics usually relies on an initial value problem which is described by a single first order ordinary differential equation. In this analysis, we will study the sensitivity analysis due to a variation of the initial condition and experimental time. …”
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Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV-Like Equation by Maria Ihsane El Bahi, Khalid Hilal

“…With the aid of infinitesimal symmetries, the vector fields and symmetry reductions of the equation are constructed, respectively; as a result, the invariant solutions are acquired in one case; we show that the KdV-like equation can be reduced to a fractional ordinary differential equation (FODE) which is connected with the Erdélyi-Kober functional derivative; for this kind of reduced form, we use the power series method for extracting the explicit solutions in the form of power series solution. …”
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Bifurcations of Tumor-Immune Competition Systems with Delay by Ping Bi, Heying Xiao

“…A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. …”
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The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation by Lu-feng Yang

“…By the Laplace transform, the ordinary differential equation about the orthogonal expansion coefficient is transformed into a linear algebraic equation system, with the coefficient matrix being a tridiagonal lower triangular matrix. …”
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New Applications of a Kind of Infinitesimal-Operator Lie Algebra by Honwah Tam, Yufeng Zhang, Xiangzhi Zhang

“…Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism. …”
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