Nonlinear variational evolution inequalities in Hilbert spaces by Jin-Mun Jeong, Doo-Hoan Jeong, Jong-Yeoul Park

“…The regular problem for solutions of the nonlinear functional differential equations with a nonlinear hemicontinuous and coercive operator A and a nonlinear term f(.,.)…”
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Linear and Riccati matrix equations by Lloyd K. Williams

“…In this paper we find exact solutions for linear ordinary differential equations of any order when they are given in matrix form, as well as for classes of Riccati matrix equations with two or three arbitrary matrix coefficients. …”
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First-Order Three-Point Boundary Value Problems at Resonance Part III by Mesliza Mohamed, Bevan Thompson, Muhammad Sufian Jusoh

“…The main purpose of this paper is to investigate the existence of solutions of BVPs for a very general case in which both the system of ordinary differential equations and the boundary conditions are nonlinear. …”
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Numerical Solution of Weakly Singular Integrodifferential Equations on Closed Smooth Contour in Lebesgue Spaces by Feras M. Al Faqih

“…The present paper deals with the justification of solvability conditions and properties of solutions for weakly singular integro-differential equations by collocation and mechanical quadrature methods. …”
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Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions by Xian-Feng Zhou, Song Liu, Zhixin Zhang, Wei Jiang

“…The monotonicity of the solutions of a class of nonlinear fractional differential equations is studied first, and the existing results were extended. …”
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A Note on the Fractional Generalized Higher Order KdV Equation by Yongyi Gu

“…It has showed that the applied method is very useful and is practically well suited for the nonlinear differential equations, those arising in mathematical physics.…”
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The Hamiltonian Structure and Algebrogeometric Solution of a 1 + 1-Dimensional Coupled Equations by Hongfei Pan, Tiecheng Xia

“…A 1 + 1-dimensional coupled soliton equations are decomposed into two systems of ordinary differential equations. The Abel-Jacobi coordinates are introduced to straighten the flows, from which the algebrogeometric solutions of the coupled 1 + 1-dimensional equations are obtained in terms of the Riemann theta functions.…”
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Mathematical modeling in autoimmune diseases: from theory to clinical application by Yaroslav Ugolkov, Yaroslav Ugolkov, Yaroslav Ugolkov, Antonina Nikitich, Antonina Nikitich, Cristina Leon, Gabriel Helmlinger, Kirill Peskov, Kirill Peskov, Kirill Peskov, Kirill Peskov, Victor Sokolov, Victor Sokolov, Alina Volkova, Alina Volkova

“…. ≥70% of the models were developed as nonlinear systems of ordinary differential equations, others – as partial differential equations, integro-differential equations, Boolean networks, or probabilistic models. …”
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Type-K Exponential Ordering with Application to Delayed Hopfield-Type Neural Networks by Bin-Guo Wang

“…Order-preserving and convergent results of delay functional differential equations without quasimonotone condition are established under type-K exponential ordering. …”
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Mathematical modelling of MHD hybrid nanofluid flow in a convergent and divergent channel under variable thermal conductivity effect by Alharbi Abdulaziz H.

“…H2O{\text{H}}_{\text{2}}\text{O}) are considered in this work. The partial differential equations modelling the problem are reduced to ordinary differential equations following the application of the similarity transformations. …”
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Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters by M. M. Rashidi, E. Momoniat, B. Rostami

“…The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM) with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid). …”
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MHD Natural Convection with Convective Surface Boundary Condition over a Flat Plate by Mohammad M. Rashidi, Mohammad Ferdows, Amir Basiri Parsa, Shirley Abelman

“…Numerical solutions of the ordinary differential equations are obtained by the Keller Box method for different values of the controlling parameters associated with the problem.…”
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Global Well-Posedness and Determining Nodes of Non-Autonomous Navier–Stokes Equations with Infinite Delay on Bounded Domains by Huanzhi Ge, Feng Du

“…The asymptotic behavior of solutions to nonlinear partial differential equations is an important tool for studying their long-term behavior. …”
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Dynamical Models of Tuberculosis and Their Applications by Carlos Castillo-Chavez, Baojun Song

“…Modelformulations involve a variety of mathematical areas, such as ODEs(Ordinary Differential Equations) (both autonomous andnon-autonomous systems), PDEs (Partial Differential Equations),system of difference equations, system of integro-differentialequations, Markov chain model, and simulation models.…”
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A Mathematical Model for a Transmissible Disease with a Variant by A. Otto, M. Amidou

“…The model is studied using the stability theory for systems of differential equations and the basic reproduction number R0. …”
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Double-Diffusive MHD Viscous Fluid Flow in a Porous Medium in the Presence of Cattaneo-Christov Theories by Bidemi Olumide Falodun, Adeola John Omowaye, Funmilayo Helen Oyelami, Homan Emadifar, Ahmed A. Hamoud, S. M. Atif

“…A set of partial differential equations governs the current design (PDEs). …”
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Optimal Homotopy Asymptotic Analysis of the Dynamics of Eyring-Powell Fluid due to Convection Subject to Thermal Stratification and Heat Generation Effect by Solomon Bati Kejela, Emiru Rufo Adula

“…The governing equations of the flow are transformed from partial differential equations into a couple of nonlinear ordinary differential equations via similarity variables. …”
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A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities by Farzad Ebrahimi, Ali Jafari

“…The governing differential equations of motion are derived based on higher order shear deformation beam theory. …”
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Benjamin-Ono Equation on a Half-Line by Nakao Hayashi, Elena I. Kaikina

“…We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.…”
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W2,p-Solvability of the Dirichlet Problem for Elliptic Equations with Singular Data by Loredana Caso, Roberta D’Ambrosio, Maria Transirico

“…We give an overview on some results concerning the unique solvability of the Dirichlet problem in W2,p, p>1, for second-order linear elliptic partial differential equations in nondivergence form and with singular data in weighted Sobolev spaces. …”
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