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.…”
Get full text

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. …”
Get full text

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.…”
Get full text

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.…”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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.…”
Get full text

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. …”
Get full text

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.…”
Get full text

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).…”
Get full text

The Rayleigh quotient and dynamic programming by Richard Bellman

“…The purpose of this paper is to derive a nonlinear partial differential equation for which λ given by (1.3), is one value of the solution. …”
Get full text

High-Frequency Electromagnetic Field Coupling to Small Antennae in a Rectangular Resonator by Sergey Tkachenko, Jürgen Nitsch, Moawia Al-Hamid

“…The integral-differential equation for the current of an electrically small antenna, inside a resonator, which is induced by given sources, is approximately solved by the so-called “Method of Small Antenna,” both for dipole and loop antennas. …”
Get full text

Perihelion Precessions of Inner Planets in Einstein’s Theory and Predicted Values for the Cosmological Constant by Alvaro H. Salas S, Jairo E Castillo H, Lorenzo J. Martınez H

“…In this paper, we obtain the approximate value of 42.9815 arcsec/century for Mercury’s perihelion precession by solving both numerically and analytically the nonlinear ordinary differential equation derived from the geodesic equation in Einstein’s Theory of Relativity. …”
Get full text

Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems by Zhenhua Hu, Shuqing Zhou

“…We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equation div(A(x,∇u))=div f(x,u), where A(x,∇u), f(x,u) are two n×N matrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.…”
Get full text