Multipoint BVP for the Langevin Equation under φ-Hilfer Fractional Operator by Mohammed A. Almalahi, Satish K. Panchal, Fahd Jarad

“…In this research paper, we consider a class of boundary value problems for a nonlinear Langevin equation involving two generalized Hilfer fractional derivatives supplemented with nonlocal integral and infinite-point boundary conditions. …”
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Least Square Homotopy Perturbation Method for Ordinary Differential Equations by Mubashir Qayyum, Imbsat Oscar

“…In this study, a new modification of the homotopy perturbation method (HPM) is introduced for various order boundary value problems (BVPs). In this modification, HPM is hybrid with least square optimizer and named as the least square homotopy perturbation method (LSHPM). …”
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Fixed Point Theory and the Liouville–Caputo Integro-Differential FBVP with Multiple Nonlinear Terms by Shahram Rezapour, Ali Boulfoul, Brahim Tellab, Mohammad Esmael Samei, Sina Etemad, Reny George

“…This work is reserved for the study of a special category of boundary value problems (BVPs) consisting of Liouville–Caputo integro-differential equations with multiple nonlinear terms. …”
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Modeling and Estimation of Thermal Flows Based on Transport and Balance Equations by Angelo Alessandri, Patrizia Bagnerini, Roberto Cianci, Roberto Revetria

“…Using such models, boundary value problems can be solved to estimate the temperatures over all the length by means of measurements taken only at the boundaries. …”
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Periodic Solutions of Second Order Nonlinear Difference Equations with Singular ϕ-Laplacian Operator by Ruyun Ma, Yanqiong Lu

“…We obtain some existence results of solutions for discrete periodic boundary value problems with singular ϕ-Laplacian operator ∇Δuk/1-κ(Δuk)2+rkuk+mk/(uk)λ=ek,   2≤k≤N-1,           u1=uN, and     Δu1=ΔuN-1 by using the upper and lower solutions method and Brouwer degree theory, where κ>0 is a constant, r=(r2,…,rN-1), m=(m2,…,mN-1), e=(e2,…,eN-1)∈RN-2, and λ>0 is a parameter. …”
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Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems by Shurong Sun, Martin Bohner, Shaozhu Chen

“…These investigations are part of a larger program which includes the following: (i) M(λ) theory for singular Hamiltonian systems, (ii) on the spectrum of Hamiltonian systems, (iii) on boundary value problems for Hamiltonian dynamic systems.…”
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Modeling and Simulation in Engineering Modeling of the Electrocoagulation Processes in Nonisothermal Conditions by Andrii Safonyk, Olena Prysiazhniuk

“…An asymptotic approximation of solutions of corresponding boundary value problems is constructed. Based on the received solutions, we conducted a computer simulation of the process of distribution of iron concentration inside the reactor that allows predicting various hydrodynamic phenomena such as internal recirculation and dead zones that affect the formation of a coagulant. …”
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Random 2D Composites and the Generalized Method of Schwarz by Vladimir Mityushev

“…First, deterministic boundary value problems are solved for all locations of inclusions, that is, for all events of the considered probabilistic space C by the generalized method of Schwarz. …”
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The Inverse Problem of Identification of Hydrogen Permeability Model by Yury V. Zaika, Natalia I. Rodchenkova, Ekaterina K. Kostikova

“…The article presents boundary value problems of hydrogen permeability and thermal desorption with dynamical boundary conditions. …”
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Exact Asymptotic Expansion of Singular Solutions for the (2+1)-D Protter Problem by Lubomir Dechevski, Nedyu Popivanov, Todor Popov

“…We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in ℝ2. …”
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Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications by Thabet Abdeljawad, Qasem M. Al-Mdallal, Mohamed A. Hajji

“…Finally, a Lyapunov type inequality for the Riemann type fractional difference boundary value problems of order 2<α≤3 is proved and the ordinary difference Lyapunov inequality then follows as α tends to 2 from right. …”
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A Novel Approximation Method for Solving Ordinary Differential Equations Using the Representation of Ball Curves by Abdul Hadi Bhatti, Sharmila Karim, Ala Amourah, Ali Fareed Jameel, Feras Yousef, Nidal Anakira

“…To demonstrate the proposed method, several boundary value problems are presented, and their performance is compared with existing methods in terms of error accuracy. …”
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A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems by S. S. Motsa

“…The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. …”
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Integration and Application of a Fabric-Based Modified Cam-Clay Model in FLAC^3D by Xiao-Wen Wang, Kai Cui, Yuan Ran, Yu Tian, Bo-Han Wu, Wen-Bin Xiao

“…In order to consider the effect of fabric anisotropy in the analysis of geotechnical boundary value problems, this study proposes a modified model based on a fabric-based modified Cam-clay model, which can account for the anisotropic response of soil. …”
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Dynamics of a diffusive age-structured HBV model with saturating incidence by Xichao Duan, Sanling Yuan, Kaifa Wang

“…We first analyze the well-posedness of the initial-boundary values problem of the model in the bounded domain $\Omega\subset\mathbb{R}^n$ and obtain an explicit formula for the basic reproductive number $R_0$ of the model. …”
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Parallel Simulation of HGMS of Weakly Magnetic Nanoparticles in Irrotational Flow of Inviscid Fluid by Kanok Hournkumnuard, Banpot Dolwithayakul, Chantana Chantrapornchai

“…The differential equations governing particle transport are solved numerically as an initial and boundary values problem by using the finite-difference method. …”
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Generating Solar Sail Trajectories in the Earth-Moon System Using Augmented Finite-Difference Methods by Geoffrey G. Wawrzyniak, Kathleen C. Howell

“…Numerical techniques to solve boundary value problems can be employed to understand this challenging dynamical regime. …”
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Nonlinear Dynamic Analysis of Plates Stiffened by Parallel Beams with Deformable Connection by J. A. Dourakopoulos, E. J. Sapountzakis

“…These tractions are integrated with respect to each half of the interface width resulting in two interface lines, along which the loading of the beams and the additional loading of the plate are defined. Six boundary value problems are formulated and solved using the analog equation method (AEM), a BEM-based method. …”
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Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem by Mohammed Hamaidi, Ahmed Naji, Fatima Ghafrani, Mostafa Jourhmane

“…In many references, both the ill-posed and inverse boundary value problems are solved iteratively. The iterative procedures are based on firstly converting the problem into a well-posed one by assuming the missing boundary values. …”
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Frozen Jacobian Multistep Iterative Method for Solving Nonlinear IVPs and BVPs by Fayyaz Ahmad, Shafiq Ur Rehman, Malik Zaka Ullah, Hani Moaiteq Aljahdali, Shahid Ahmad, Ali Saleh Alshomrani, Juan A. Carrasco, Shamshad Ahmad, Sivanandam Sivasankaran

“…In this paper, we present and illustrate a frozen Jacobian multistep iterative method to solve systems of nonlinear equations associated with initial value problems (IVPs) and boundary value problems (BVPs). We have used Jacobi-Gauss-Lobatto collocation (J-GL-C) methods to discretize the IVPs and BVPs. …”
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