Approximate Solution of Tuberculosis Disease Population Dynamics Model by Abdon Atangana, Necdet Bildik

“…We examine possible approximate solutions of both integer and noninteger systems of nonlinear differential equations describing tuberculosis disease population dynamics. …”
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Modeling of the migration of endothelial cells on bioactive micropatterned polymers by Thierry Colin, Marie-Christine Durrieu, Julie Joie, Yifeng Lei, Youcef Mammeri, Clair Poignard, Olivier Saut

“…It isbased on a system of partial differential equations ofPatlak-Keller-Segel type that describes theevolution of the cell densities. …”
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Existence and H-U Stability of Solution for Coupled System of Fractional-Order with Integral Conditions Involving Caputo-Hadamard Derivatives, Hadamard Integrals by Muath Awadalla, Muthaian Subramanian, Murugesan Manigandan, Kinda Abuasbeh

“…In this article, the primary focus of our study is to investigate the existence, uniqueness, and Ulam-Hyers stability results for coupled fractional differential equations of the Caputo-Hadamard type that are supplemented with Hadamard integral boundary conditions. …”
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Variable Step Size Adams Methods for BSDEs by Qiang Han

“…For backward stochastic differential equations (BSDEs), we construct variable step size Adams methods by means of Itô–Taylor expansion, and these schemes are nonlinear multistep schemes. …”
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Nonexistence of Global Solutions for Coupled System of Pseudoparabolic Equations with Variable Exponents and Weak Memories by Kh. Zennir, H. Dridi, S. Alodhaibi, S. Alkhalaf

“…The nonsolvability of boundary value problem for damped pseudoparabolic differential equations with variable exponents is investigated. …”
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On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory by Geni Gupur

“…We describe the point spectrum of the generator of a C0-semigroup associated with the M/M/1 queueing model that is governed by an infinite system of partial differential equations with integral boundary conditions. …”
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Fixed Point Theorems of Superlinear Operators with Applications by Shaoyuan Xu, Yan Han

“…The results are applied to nonlinear integral equations and partial differential equations.…”
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Stability and persistence in ODE modelsfor populations with many stages by Guihong Fan, Yijun Lou, Horst R. Thieme, Jianhong Wu

“…A model of ordinary differential equations is formulated for populationswhich are structured by many stages. …”
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Hyperbolic differential-operator equations on a whole axis by Yakov Yakubov

“…Then we show applications of obtained abstract results to hyperbolic differential equations which, in particular, may represent the longitudinal displacements of an inhomogeneous rod under the action of forces at the two ends which are proportional to the acceleration.…”
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Valuation of Credit Derivatives with Multiple Time Scales in the Intensity Model by Beom Jin Kim, Chan Yeol Park, Yong-Ki Ma

“…We propose approximate solutions for pricing zero-coupon defaultable bonds, credit default swap rates, and bond options based on the averaging principle of stochastic differential equations. We consider the intensity-based defaultable bond, where the volatility of the default intensity is driven by multiple time scales. …”
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Building Infinitely Many Solutions for Some Model of Sublinear Multipoint Boundary Value Problems by Guy Aymard Degla

“…The idea of the proof is of independent interest since it shows a constructive way to have ordinary differential equations with multiple solutions.…”
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Preliminary Hybrid Modeling of the Panama Canal: Operations and Salinity Diffusion by Luis Rabelo, Mario Marin, Petros Xanthopoulos, Carlos Arellano Lennox, Pedro Coiduras, Bernardo Campos, Luz Andrade, Ricardo Collins, Erwin Atencio, Daryelis Pitty

“…This was accomplished by generating an operational discrete-event simulation model and a continuous simulation model based on differential equations, which modeled the salinity diffusion in the lakes. …”
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Dynamics of a delay Schistosomiasis model in snail infections by Chunhua Shan, Hongjun Gao, Huaiping Zhu

“…In this paper we modify and study a system of delay differential equations model proposed by Nåsell and Hirsch (1973) for the transmission dynamics of schistosomiasis. …”
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Global Stability of HIV-1 Infection Model with Two Time Delays by Hui Miao, Xamxinur Abdurahman, Ahmadjan Muhammadhaji

“…We investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. …”
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The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions by Shoukry Ibrahim Atia El-Ganaini

“…The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1)-dimensional hyperbolic nonlinear Schrodinger (HNLS) equation, the generalized nonlinear Schrodinger (GNLS) equation with a source, and the higher-order nonlinear Schrodinger equation in nonlinear optical fibers. …”
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Vibration Suppression Control of a Flexible Gantry Crane System with Varying Rope Length by Tung Lam Nguyen, Trong Hieu Do, Hong Quang Nguyen

“…The equations of motion consist of a system of ordinary and partial differential equations. Lyapunov’s direct method is used to derive the control located at the trolley end that can precisely position the gantry payload and minimize vibrations. …”
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Error Analysis of Galerkin's Method for Semilinear Equations by Tadashi Kawanago

“…Some of our results may be applicable for investigating the quality of numerical verification methods for solutions of ordinary and partial differential equations.…”
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Global Existence for the 3D Tropical Climate Model with Small Initial Data in H˙1/2ℝ3∗ by Hui Zhang, Juan Xu

“…The well-posedness problem is an important but challenging research topic in nonlinear partial differential equations. In this paper, we establish a global-in-time existence result of strong solutions for small initial data in terms of the H˙1/2ℝ3 norm on three-dimensional tropical climate model with viscosities by derive a blow-up criterion combine with energy estimates. …”
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Skew Circulant Type Matrices Involving the Sum of Fibonacci and Lucas Numbers by Zhaolin Jiang, Yunlan Wei

“…Skew circulant and circulant matrices have been an ideal research area and hot issue for solving various differential equations. In this paper, the skew circulant type matrices with the sum of Fibonacci and Lucas numbers are discussed. …”
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Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect Spiracle by S. M. Simelane, S. Abelman, F. D. Duncan

“…Here we investigate and analyze this interaction by deriving a system of ordinary differential equations for oxygen, carbon dioxide, and water vapor. …”
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