Improving diversification by a hybrid bat-Nelder-Mead algorithm and DDE for rapid convergence to solve global optimization by Enas Suhail, Mahmoud El-Alem, Omar Bazighifan, Ahmed Zekri

“…Delay differential equations and algorithms hold a crucial position in the exploration of some biological systems and several models in real-world applications. …”
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A simple model of carcinogenic mutations with time delay and diffusion by Monika Joanna Piotrowska, Urszula Foryś, Marek Bodnar, Jan Poleszczuk

“…In the paper we consider a system of delay differential equations (DDEs) of Lotka-Volterra type with diffusion reflecting mutations from normal to malignant cells. …”
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Study of the Radical Chain Mechanism of Hydrocarbon Oxidation for In Situ Combustion Process by Alexandra Ushakova, Vladislav Zatsepin, Mikhail Varfolomeev, Dmitry Emelyanov

“…The system of differential equations based on the equations of oxidation reactions was solved. …”
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Optimal Control of Endemic Epidemic Diseases With Behavioral Response by Francesco Parino, Lorenzo Zino, Alessandro Rizzo

“…In particular, we propose a parsimonious model that couples an epidemic compartmental model with a population game that captures the behavioral response, obtaining a nonlinear system of ordinary differential equations. Grounded on prevalence-elastic behavior—the empirically proven assumption that the disease prevalence affects the adherence to self-protective behavior—we consider a nontrivial negative feedback between contagions and adoption of self-protective behavior. …”
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Insight on the complete process of photoacoustic generation and propagation of cerebrovascular in brain via multi-physics coupling method by Shangkun Hou, Anzhi Lv, Jiabin Lin, Bokang You, Shuaixin Huang, Xianlin Song

“…The diffusion equation is approximated by the partial differential equations in the form of coefficients in the mathematical module of COMSOL to describe laser propagation in brain tissue. …”
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Modeling bacterial attachment to surfaces as an early stage of biofilm development by Fadoua El Moustaid, Amina Eladdadi, Lafras Uys

“…While much is known about the later stages of biofilm formation, less is known about its initiation which is an important first step in the biofilm formation.In this paper, we develop a non-linear system of partial differential equations of Keller-Segel type model in one-dimensional space, which couples the dynamics of bacterial movement to that of the sensing molecules. …”
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Numerical Solutions of Certain New Models of the Time-Fractional Gray-Scott by Sami Aljhani, Mohd Salmi Md Noorani, Khaled M. Saad, A. K. Alomari

“…The fractional homotopy analysis transformation method algorithm can be easily applied for singular and nonsingular fractional derivative with partial differential equations, where a few terms of series solution are good enough to give an accurate solution.…”
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Dynamic Characteristics of a Cylindrical Roller Bearing with Cage Cracks by Yang Yang, Xiaoye Qi, Yongjie Wang, Meiling Wang, Baogang Wen, Jingyu Zhai

“…The derived dynamic differential equations of cylindrical roller bearings were solved by means of the modified Newton–Raphson iterative algorithm and the BDF predictive correction algorithm with automatic variable order and step length. …”
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A hybrid fractional model for cervical cancer due to human papillomavirus infection by Ali Akgül, Nauman Ahmed, Sadiya Ali Rano, Qasem Al-Mdallal

“…The proposed model consists of three fractional order nonlinear differential equations. The Grünwald Letnikov method is used to approximate the hybrid operator. …”
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Applying Fourier Neural Operator to insect wingbeat sound classification: Introducing CF-ResNet-1D by Béla J. Szekeres, Máté Natabara Gyöngyössy, János Botzheim

“…Despite recent advancements in Deep Learning, Fourier Neural Operators (FNO), efficient for solving Partial Differential Equations due to their global spectral representations, have yet to be thoroughly explored for real-world time series classification or regression tasks. …”
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Solutions of Cauchy Problems for the Caudrey–Dodd–Gibbon–Kotera–Sawada Equation in Three Spatial and Two Temporal Dimensions by Yufeng Zhang, Linlin Gui

“…Fokas has obtained integrable nonlinear partial differential equations (PDEs) in 4 + 2 dimensions by complexifying the independent variables. …”
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Explicit scheme based on integral transforms for estimation of source terms in diffusion problems in heterogeneous media by André José Pereira de Oliveira, Luiz Alberto da Silva Abreu, Diego Campos Knupp

“… The estimation of source terms present in differential equations has various applications, ranging from structural assessment, industrial process monitoring, equipment failure detection, environmental pollution source detection to identification applications in medicine. …”
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Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method by Wafaa B. Rabie, Hamdy M. Ahmed, Taher A. Nofal, E. M. Mohamed

“…Higher-order nonlinear partial differential equations, such as the eighth-order Kac-Wakimoto model, are useful for studying wave turbulence in fluids, where energy transfers across a range of wave numbers. …”
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Influence of different delays on mixed types of oscillations under limited excitation by A. A. Alifov

“…With the account of the interaction with the energy source, the known calculation scheme (or model) of a mechanical frictional self-oscillating system serves as a unified basis for considering all types of MOs. Nonlinear differential equations of motion valid for all types of MOs with their respective solutions were presented, from which the relations for any certain type of MO are derived as special cases. …”
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Time-periodic dynamics in COVID-19 transmission considering the impact of population disbelief and fear by Mahmoud A. Ibrahim, Attila Dénes

“…Our model utilizes a system of differential equations that incorporates the impact of both contagious fear and contagious disbelief surrounding the disease on its transmission dynamics. …”
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Epidemic spread of influenza viruses: The impact of transient populations on disease dynamics by Karen R. Ríos-Soto, Baojun Song, Carlos Castillo-Chavez

“…A metapopulation framework based on a system of nonlinear ordinary differential equations is used to study the transmission dynamics and control of avian diseases. …”
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Evaluation of the increased load bearing capacity of steel beams strengthened with pre-stressed FRP laminates by S. Bennati, D. Colonna, P.S. Valvo

“…The model is described by a set of differential equations with suitable boundary conditions. …”
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Nonlinear Dynamics of the High-Speed Rotating Plate by Minghui Yao, Li Ma, Wei Zhang

“…Galerkin approach is applied to discretize the partial differential governing equations of motion to ordinary differential equations. Asymptotic perturbation method is exploited to derive four-degree-of-freedom averaged equation for the case of 1 : 3 internal resonance-1/2 sub-harmonic resonance. …”
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Circular thin plates buckling analysis with HRPIM method by Baid Sokayna, Hilali Youssef, Mesmoudi Saïd, Bourihane Oussama

“…The governing partial differential equations are discretized using the Galerkin method and solved by combining a Taylor series expansion with a continuation procedure. …”
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$\phi $-FEM for the heat equation: optimal convergence on unfitted meshes in space by Duprez, Michel, Lleras, Vanessa, Lozinski, Alexei, Vuillemot, Killian

“…Thanks to a finite element method, we solve numerically parabolic partial differential equations on complex domains by avoiding the mesh generation, using a regular background mesh, not fitting the domain and its real boundary exactly. …”
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