Physiology-informed regularisation enables training of universal differential equation systems for biological applications. by Max de Rooij, Balázs Erdős, Natal A W van Riel, Shauna D O'Donovan

“…The integration of neural networks and mechanistic models, forming universal differential equation (UDE) models, enables the automated learning of unknown model terms with less data than neural networks alone. …”
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Positive Solutions to Periodic Boundary Value Problems of Nonlinear Fractional Differential Equations at Resonance by Lei Hu

“…International Journal of Differential Equations…”
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Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions by S. Akhlaghi, M. Tavassoli Kajani, M. Allame

“…In this paper, we derive a spectral collocation method for solving fractional-order integro-differential equations by using a kind of Müntz orthogonal functions that are defined on 0,1 and have simple and real roots in this interval. …”
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Positive Solutions for Systems of Nonlinear Higher Order Differential Equations with Integral Boundary Conditions by Yaohong Li, Xiaoyan Zhang

“…By constructing some general type conditions and using fixed point theorem of cone, this paper investigates the existence of at least one and at least two positive solutions for systems of nonlinear higher order differential equations with integral boundary conditions. …”
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Multivalued semilinear neutral functional differential equations with nonconvex-valued right-hand side by M. Benchohra, E. Gatsori, S. K. Ntouyas

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Convergence of Variational Iteration Method for Solving Singular Partial Differential Equations of Fractional Order by Asma Ali Elbeleze, Adem Kılıçman, Bachok M. Taib

“…We are concerned here with singular partial differential equations of fractional order (FSPDEs). The variational iteration method (VIM) is applied to obtain approximate solutions of this type of equations. …”
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Positive Solutions for a System of Hadamard-Type Fractional Differential Equations with Semipositone Nonlinearities by Youzheng Ding, Jiqiang Jiang, Donal O’Regan, Jiafa Xu

“…In this paper, we use the fixed-point index and nonnegative matrices to study the existence of positive solutions for a system of Hadamard-type fractional differential equations with semipositone nonlinearities.…”
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Fractional Variational Iteration Method for Solving Fractional Partial Differential Equations with Proportional Delay by Brajesh Kumar Singh, Pramod Kumar

“…International Journal of Differential Equations…”
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Existence and Stability for a Nonlinear Coupled p-Laplacian System of Fractional Differential Equations by Merfat Basha, Binxiang Dai, Wadhah Al-Sadi

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Research on boundary control of vehicle-mounted flexible manipulator based on partial differential equations. by Yuzhi Tang

“…We present a novel mathematical model, derived using Hamilton's principle, which simplifies the analysis of the arm's dynamic behaviors by employing partial differential equations (PDEs). This model allows us to understand how these arms behave over time and space, classifying them as distributed parameter systems. …”
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Numerical Investigation of Fractional-Order Differential Equations via φ-Haar-Wavelet Method by F. M. Alharbi, A. M. Zidan, Muhammad Naeem, Rasool Shah, Kamsing Nonlaopon

“…In this paper, we propose a novel and efficient numerical technique for solving linear and nonlinear fractional differential equations (FDEs) with the φ-Caputo fractional derivative. …”
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Stochastic differential equations to model influenza transmission with continuous and discrete-time Markov chains by Kazi Mehedi Mohammad, Md. Kamrujjaman

“…Since the basic reproduction number R0 is not sufficient to predict the outbreak, we apply the discrete-time Markov chain (DTMC), continuous-time Markov chain (CTMC), and Itô stochastic differential equations (SDEs) to calculate the probability of the disease outbreak. …”
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Multiscale effective connectivity analysis of brain activity using neural ordinary differential equations. by Yin-Jui Chang, Yuan-I Chen, Hannah M Stealey, Yi Zhao, Hung-Yun Lu, Enrique Contreras-Hernandez, Megan N Baker, Edward Castillo, Hsin-Chih Yeh, Samantha R Santacruz

“…Here we introduce a neurobiological-driven deep learning model, termed multiscale neural dynamics neural ordinary differential equation (msDyNODE), to describe multiscale brain communications governing cognition and behavior. …”
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Exponential Stability for an Opinion Formation Model with a Leader Associated with Fractional Differential Equations by Dussadee Somjaiwang, Parinya Sa Ngiamsunthorn

“…International Journal of Differential Equations…”
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A novel analytical treatment for the Ambartsumian delay differential equation with a variable coefficient by Rana M. S. Alyoubi, Abdelhalim Ebaid, Essam R. El-Zahar, Mona D. Aljoufi

“…The Ambartsumian delay differential equation with a variable coefficient is considered in this paper. …”
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Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection by Xinchao Yang, Xiju Zong, Xingong Cheng, Zhenlai Han

“…The stability and bifurcation analysis for a delay differential equation of hepatitis B virus infection is investigated. …”
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Multiplicity of Positive Solutions for Fractional Differential Equation with p-Laplacian Boundary Value Problems by Sabbavarapu Nageswara Rao

“…International Journal of Differential Equations…”
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A Note on Four-Dimensional Symmetry Algebras and Fourth-Order Ordinary Differential Equations by A. Fatima, Muhammad Ayub, F. M. Mahomed

“…We provide a supplementation of the results on the canonical forms for scalar fourth-order ordinary differential equations (ODEs) which admit four-dimensional Lie algebras obtained recently. …”
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A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods by F. Z. Geng, X. M. Li

“…The quasilinearization technique is used to reduce the Riccati differential equation to a sequence of linear problems. The resulting sets of differential equations are treated by using reproducing kernel method. …”
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Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method by Asfaw Tsegaye Moltot, Alemayehu Tamirie Deresse

“…Furthermore, the findings indicate that the recommended strategy is encouraging for solving other types of nonlinear delay differential equations.…”
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