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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Nematic Liquid Crystal Locking Menisci by Milan Svetec, Mitja Slavinec

“…The resulting Euler-Lagrange differential equation is solved numerically. We determine conditions for the defects to be trapped by the meniscus.…”
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Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator by Sombir Dhaniya, Anoop Kumar, Aziz Khan, Thabet Abdeljawad, Manar A. Alqudah

“…In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. …”
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Study of Time Evolution for Approximation of Two-Body Spinless Salpeter Equation in Presence of Time-Dependent Interaction by Hadi Sobhani, Hassan Hassanabadi

“…We use the Lewis-Riesenfeld dynamical invariant method and series solution to obtain the solutions of the differential equation. We have also done some calculations in order to derive the time evolution operator for the considered problem.…”
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A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables by Yong Yan

“…We apply our result to a boundary value problem of a partial differential equation with maxima for uniqueness.…”
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The Role of Numerical Methods in the Sensitivity Analysis of a Density Parameter in a Passivation Rate Interaction by EN Ekaka-a, EO Chukwuocha, NM Nafo

“…The mathematical modelling of physiochemical interaction in the framework of industrial and environmental physics which relies on an initial value problem is defined by a first order ordinary differential equation. Two numerical methods of studying sensitivity analysis of physiochemical interaction data are developed. …”
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Further studies of fully developed flow through ducts of arbitrary section by the contour line-conformal mapping technique by J. Mazumdar, D. Hopkins

“…The amplitude of the oscillatory velocity is then obtained from an ordinary integro-differential equation. Several examples of a practical nature are given, with some that have not yet been discussed in the literature. …”
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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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Solvability of Three-Point Boundary Value Problems at Resonance with a p-Laplacian on Finite and Infinite Intervals by Hairong Lian, Patricia J. Y. Wong, Shu Yang

“…Three-point boundary value problems of second-order differential equation with a p-Laplacian on finite and infinite intervals are investigated in this paper. …”
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On the spectrum of a stationary problem with nonlocal integral type boundary condition by Sigita Pečiulytė, Olga Štikonienė, Artūras Štikonas

“… We investigated a eigenvalue problem for simple second order ordinary differential equation with one inte­gral type nonlocal boundary condition. …”
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New Exact Solutions of Burgers’ Equation Using Power Index Method by Khalil Ahmad, Khudija Bibi

“…In this method, we choose suitable indexes of independent variables and similarity transformation so that the partial differential equation may be converted into ODE. We have obtained analytic solution of the ODE by using symbolic package Maple. …”
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Enhancement of stability of metastable states in the presence of Lévy noise by Alexander A. Dubkov, Claudio Guarcello, Bernardo Spagnolo

“…Starting from the fractional Fokker-Planck equation, we derive an integro-differential equation along with the necessary conditions to calculate the mean residence time of a particle within a fixed interval. …”
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Solutions and Conservation Laws of a (2+1)-Dimensional Boussinesq Equation by Letlhogonolo Daddy Moleleki, Chaudry Masood Khalique

“…We study a nonlinear evolution partial differential equation, namely, the (2+1)-dimensional Boussinesq equation. …”
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Different Physical Structures of Solutions for a Generalized Resonant Dispersive Nonlinear Schrödinger Equation with Power Law Nonlinearity by K. S. Al-Ghafri

“…Based on simple mathematical techniques, the complicated form of the GRD-NLSE is reduced to an ordinary differential equation (ODE) which has a variety of solutions. …”
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Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods by Özkan Güner, Dursun Eser

“…As a result, these methods can also be applied to other nonlinear fractional differential equations.…”
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Dual Approximate Solutions of the Unsteady Viscous Flow over a Shrinking Cylinder with Optimal Homotopy Asymptotic Method by Vasile Marinca, Remus-Daniel Ene

“…The nonlinear differential equation is obtained by means of the similarity transformation. …”
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Basic Properties of Incomplete Macdonald Function with Applications by Jian-Jun Shu, Kunal Krishnaraj Shastri

“…This paper also shows that the incomplete Macdonald function, as a simple closed-form expression, is a particular solution to a parabolic partial differential equation, which arises naturally in a wide variety of transient and diffusion-related phenomena.…”
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Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate by Chun Lu

“…Finally, we propose a definition of the solution to an impulsive stochastic functional differential equation with Markovian switching (ISFDM).…”
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