Algebro-Geometric Solutions of a (2+1)-Dimensional Integrable Equation Associated with the Ablowitz-Kaup-Newell-Segur Soliton Hierarchy by Xiaohong Chen

“…The (2+1)-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known (1+1)-dimensional soliton equations associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy. …”
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Fuzzy Optimal Control Problem of Several Variables by Altyeb Mohammed Mustafa, Zengtai Gong, Mawia Osman

“…Also, we define fuzzy optimal control problems involving isoperimetric constraints and higher order differential equations. Then, we convert these problems to fuzzy optimal control problems of several variables in order to solve these problems using the same solution method. …”
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New Contractive Mappings and Their Fixed Points in Branciari Metric Spaces by Hayel N. Saleh, Mohammad Imdad, Thabet Abdeljawad, Mohammad Arif

“…Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results.…”
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Interpolating Stabilized Element Free Galerkin Method for Neutral Delay Fractional Damped Diffusion-Wave Equation by Mostafa Abbaszadeh, Mehdi Dehghan, Mahmoud A. Zaky, Ahmed S. Hendy

“…A numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative is constructed. …”
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Dynamical Behaviors of the Stochastic Hopfield Neural Networks with Mixed Time Delays by Li Wan, Qinghua Zhou, Zhigang Zhou, Pei Wang

“…By employing the theory of stochastic functional differential equations and linear matrix inequality (LMI) approach, some novel criteria on asymptotic stability, ultimate boundedness, and weak attractor are derived. …”
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On some classes of almost periodic functions in abstract spaces by Dariusz Bugajewski, Gaston M. N'Guérékata

“…Some applications to ordinary as well as partial differential equations are presented. Moreover, we introduce the class of the so-called asymptotically C(n)-almost periodic functions and give some of their properties.…”
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Pseudo-State Sliding Mode Control of Fractional SISO Nonlinear Systems by Bao Shi, Jian Yuan, Chao Dong

“…Firstly, a stable fractional sliding mode surface is constructed based on the Routh-Hurwitz conditions for fractional differential equations. Secondly, a sliding mode control law is designed using the theory of Mittag-Leffler stability. …”
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Thermal effects of ternary Casson nanofluid flow over a stretching sheet: An investigation of Thomson and Troian velocity slip by Musharafa Saleem, A. Al-Zubaidi, Neyara Radwan, S. Saleem, Hind Adawi

“…This leads to a set of partial differential equations (PDEs) based mathematical models transformed into ordinary differential equations (ODEs)-appropriate similarity transformation. …”
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On the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes by Pramod Pandey

“… In this article, we have presented a variable step finite difference method for solving second order boundary value problems in ordinary differential equations. We have discussed the convergence and established that proposed has at least cubic order of accuracy. …”
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Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications by Jiang Zhu, Dongmei Liu

“…By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.…”
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The Solutions of Mixed Monotone Fredholm-Type Integral Equations in Banach Spaces by Hua Su

“…Our results are even new to ϕ convex and -φ concave quasi operator, and then we apply these results to the two-point boundary value problem of second-order nonlinear ordinary differential equations in the ordered Banach spaces.…”
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Exact Solutions of the 3D Fractional Helmholtz Equation by Fractional Differential Transform Method by Saleh Alshammari, Salah Abuasad

“…Two examples are given to prove the proficiency of the suggested method, to resolve diverse categories of fractional partial differential equations.…”
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Fractional Integration via Picard Method for Solving Fractional Differential-Algebraic Systems by Susan H. Mohammad, Abdulghafor Mohammed Al-Rozbayani

“…In this paper, we applied an efficient integrative method called the fractional Picard method to find the approximate solution to a system of fractional algebraic differential equations (SFADEs). By comparing the results with the exact solution, it was found that this method is highly efficient for finding solutions. …”
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Registration-Based Morphing of Active Contours for Segmentation of CT Scans by Yuan-Nan Young, Doron Levy

“…We present a new algorithm for segmenting organs in CT scans forradiotherapy treatment planning.Given a contour of an organ that is segmentedin one image, our algorithm proceeds tosegment contours that identify the same organ inthe consecutive images.Our technique combines partial differential equations-based morphing activecontours with algorithms for joint segmentation and registration. …”
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Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity by Yu G. Smirnov, D. V. Valovik

“…This electromagnetic problem is reduced to the nonlinear boundary eigenvalue problem for ordinary differential equations. It is necessary to find eigenvalues of the problem (propagation constants of an electromagnetic wave). …”
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Epidemic models with differential susceptibility and stagedprogression and their dynamics by James M. Hyman, Jia Li

“…We formulate and study epidemic models with differential susceptibilities andstaged-progressions, based on systems of ordinary differential equations, fordisease transmission where the susceptibility of susceptible individuals varyand the infective individuals progress the disease gradually through stageswith different infectiousness in each stage. …”
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Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar by M.-C. Casabán, J.-C. Cortés, B. García-Mora, L. Jódar

“…Using previous results about random ordinary differential equations, a closed form solution stochastic process is firstly obtained. …”
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Maximal regular boundary value problems in Banach-valued function spaces and applications by Veli B. Shakhmurov

“…In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value problems for parabolic equations, and their systems on cylindrical domain are studied.…”
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A leaky integrate-and-fire model with adaptation for the generation of a spike train by Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora

“…We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. …”
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Analytical Solution of Nonlinear Dynamics of a Self-Igniting Reaction-Diffusion System Using Modified Adomian Decomposition Method by Felicia Shirly Peace, Narmatha Sathiyaseelan, Lakshmanan Rajendran

“…An approximate analytical method (modified Adomian decomposition method) is used to solve nonlinear differential equations under steady-state condition. Analytical expressions for concentrations of the gas reactant and the temperature have been derived for Lewis number (Le) and parameters β, γ, and ϕ2. …”
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