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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BUCKLING OF BEAMS WITH A BOUNDARY ELEMENT TECHNIQUE by ABDERRAZEK MESSAOUDI, LASZLO PETER KISS

“…If the Green functions of these boundary value problems are known, the differential equations of the stability problems that contain the critical load sought can be turned into eigenvalue problems given by homogeneous Fredholm integral equations. …”
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Limit Cycles of a Class of Perturbed Differential Systems via the First-Order Averaging Method by Amor Menaceur, Salah Mahmoud Boulaaras, Amar Makhlouf, Karthikeyan Rajagobal, Mohamed Abdalla

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The effect of time delay in plant--pathogen interactions with host demography by Bruno Buonomo, Marianna Cerasuolo

“…We replace this hypothesis in the framework of delay differential equations by proposing a delayed epidemic model for plant--pathogen interactions with host demography. …”
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Strong Convergence of a New Hybrid Iterative Scheme for Nonexpensive Mappings and Applications by Jie Jia, Khurram Shabbir, Khushdil Ahmad, Nehad Ali Shah, Thongchai Botmart

“…By using the Picard-Thakur hybrid iterative scheme, we can find the solution of delay differential equations and also prove some convergence results for nonexpansive mapping in a uniformly convex Banach space.…”
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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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Numerical Solutions of a Variable-Order Fractional Financial System by Shichang Ma, Yufeng Xu, Wei Yue

“…Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the method is also estimated numerically. …”
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A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method by R. Ellahi

“…Due to the nonlinear, coupled, and highly complicated nature of partial differential equations, finding an analytical solution is not an easy task. …”
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Sensitivity and Optimal Control Analysis of an Extended SEIR COVID-19 Mathematical Model by C. M. Wachira, G. O. Lawi, L. O. Omondi

“…In this paper, a mathematical model based on a system of ordinary differential equations is developed with vaccination as an intervention for the transmission dynamics of coronavirus 2019 (COVID-19). …”
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Novel exact solutions for PDEs with mixed boundary conditions by Mark Craddock, Martino Grasselli, Andrea Mazzoran

“…Abstract We develop methods for the solution of inhomogeneous Robin-type boundary value problems (BVPs) that arise for certain linear parabolic partial differential equations (PDEs) on a half-line, as well as a second-order generalization. …”
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Analysis of the Nonlinear Structural-Acoustic Resonant Frequencies of a Rectangular Tube with a Flexible End Using Harmonic Balance and Homotopy Perturbation Methods by Y. Y. Lee

“…The structural acoustic problem considered in this study is the nonlinear resonant frequencies of a rectangular tube with one open end, one flexible end, and four rigid side walls A multiacoustic single structural modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibration of the flexible end and acoustic pressure induced within the tube. …”
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Physics Informed by Deep Learning: Numerical Solutions of Modified Korteweg-de Vries Equation by Yuexing Bai, Temuer Chaolu, Sudao Bilige

“…The method that we used in this paper had demonstrated the powerful mathematical and physical ability of deep learning to flexibly simulate the physical dynamic state represented by differential equations and also opens the way for us to understand more physical phenomena later.…”
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A Study of a Diseased Prey-Predator Model with Refuge in Prey and Harvesting from Predator by Ahmed Sami Abdulghafour, Raid Kamel Naji

“…The proposed mathematical model is consisting of three first-order nonlinear ordinary differential equations, which describe the interaction among the healthy prey, infected prey, and predator. …”
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Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysis by Ravindra Rao, Jagan Mohan Jonnalagadda

“…We study the existence and uniqueness of solutions to a particular class of two-point boundary value problems involving fourth-order ordinary differential equations. Such problems have exciting applications for modeling the deflections of beams. …”
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On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods by A. K. Gupta, S. Saha Ray

“…Haar wavelet method is an efficient numerical method for the numerical solution of arbitrary order partial differential equations like Burgers-Fisher and generalized Fisher equations. …”
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Mixed Convection over an Inclined Wavy Surface in a Nanofluid Saturated Non-Darcy Porous Medium with Radiation Effect by Darbhasayanam Srinivasacharya, Poshala Vijay Kumar

“…The governing equations are transformed into a set of ordinary differential equations using the appropriate similarity transformation and then solved using the successive linearization method. …”
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Convertible Bonds with Higher Loan Rate: Model, Valuation, and Optimal Strategy by Haiyang Wang, Zhen Wu

“…We study the pricing problem for convertible bonds via backward stochastic differential equations (BSDEs). By virtue of reflected BSDEs and Malliavin derivatives, we establish the formulae for the fair price of convertible bonds and the hedging portfolio strategy explicitly. …”
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Vibration Suppression of a Coupled Aircraft Wing with Finite-Time Convergence by Yiming Liu, Zhifeng Tan, Xiaofen Yang, Xiaowei Wang

“…Since the model is modeled by partial differential equations, the traditional control design scheme based on the ordinary differential equation model is not applicable, and the control law design becomes very complex. …”
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Novel Stability Criteria of Nonlinear Uncertain Systems with Time-Varying Delay by Yali Dong, Shengwei Mei, Xueli Wang

“…By constructing the proposed Lyapunov-Krasovskii functional approach, continuous state feedback controllers are put forward, and the criteria which guarantee the exponential stabilization of the nonlinear systems with uncertainties and time-varying delay are established in terms of solutions to the standard Riccati differential equations. Furthermore, based on the Lyapunov method and the linear matrix inequality approach, the sufficient conditions of exponential stability for a class of uncertain systems with time-varying delays and nonlinear perturbations are derived. …”
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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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