Unsteady flow and heat transfer optimization of viscous fluid with bioconvection over a rotating stretchable disk and gyrotactic motile microorganisms by Mazhar Hussain, Samya Shahid, Noreen Sher Akbar, Mohammed Kbiri Alaoui

“…Impact of unsteady variable (S), disk stretching variable (α), Prandtl number (Pr), Lewis number (Le) are analyzed graphically to understand the thermal and flow behavior. The boundary value problem is numerically solved using shooting method with Runga-Kutta technique by converting equations into initial value problem. …”
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Mixed Convective-Radiative Dissipative Magnetized Micropolar Nanofluid Flow over a Stretching Surface in Porous Media with Double Stratification and Chemical Reaction Effects: ADM-... by P. K. Pattnaik, M. M. Bhatti, S. R. Mishra, Munawwar Ali Abbas, O. Anwar Bég

“…An innovative semi-numerical methodology combining the Adomian decomposition method (ADM) with Padé approximants and known as ADM-Padé is deployed to solve the emerging nonlinear ordinary differential boundary value problem with appropriate wall and free stream conditions in MATLAB software. …”
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Experimental and Theoretical Study on the Failure of Sandwich Specimens with Tabs under Four-Point Bending by V. N. Paimushin, S. A. Kholmogorov, M. V. Makarov, N. V. Levshonkova

“…This method involved reducing the original boundary value problem to integro-algebraic equations with Volterra-type operators of the second kind and additional relations for determining the unknown integration constants. …”
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Residual Energy and Broken Symmetry in Reduced Magnetohydrodynamics by S. Dorfman, M. Abler, S. Boldyrev, C. H. K. Chen, S. Greess

“…These modes have net-positive residual energy in the equivalent boundary value problem, suggesting that the initial value setup is a better match for solar wind turbulence.…”
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Degenerate Differential Operators with Parameters by Veli B. Shakhmurov

“…The nonlocal boundary value problems for regular degenerate differential-operator equations with the parameter are studied. …”
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The Conical Radial Basis Function for Partial Differential Equations by J. Zhang, F. Z. Wang, E. R. Hou

“…The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or quasi-uniformly in the physical domain of the boundary value problems in question, we consider three different Chebyshev-type schemes to generate the collocation points. …”
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Periodic solutions of nonlinear differential equations by Xiaojing Yang

“…The periodic boundary value problems of a class of nonlinear differential equations are investigated.…”
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Periodic Problems of Difference Equations and Ergodic Theory by B. A. Biletskyi, A. A. Boichuk, A. A. Pokutnyi

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An essay on the foundations of variational methods: Exploring Sobolev Spaces for boundary integral equations by Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales

“…The results provide significant advancements in the mathematical understanding of boundary value problems in non-smooth domains, with potential applications in various fields of physics and engineering. …”
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Modified α-Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner Equation by Abdulghafor M. Al-Rozbayani, Ahmed Farooq Qasim

“…In this article, we present a novel enhancement to the α-parameterized differential transform method (PDTM) for solving nonlinear boundary value problems. The proposed method is applied to solve the generalized Gardner equation by utilizing genetic algorithms to obtain optimal parameter values. …”
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Variational Approach to Impulsive Problems: A Survey of Recent Results by Fang-fang Liao, Juntao Sun

“…We present a survey on the existence of nontrivial solutions to impulsive differential equations by using variational methods, including solutions to boundary value problems, periodic solutions, and homoclinic solutions.…”
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Parameters and solutions of linear and nonlinear oscillators by Rina Ling

“…Relationship between existence of solutions for certain classes of nonlinear boundary value problems and the smallest or the largest eigenvalue of the corresponding linear problem is obtained. …”
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An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs by Eman S. Alaidarous, Malik Zaka Ullah, Fayyaz Ahmad, A.S. Al-Fhaid

“…In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. …”
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Eigenfunction Expansions of Impulsive Dynamic Sturm-Liouville Problems by Bilender Allahverdiev, Hüseyin Tuna, Hamlet A Isayev

“…This paper studies impulsive dynamic Sturm-Liouville boundary value problems. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.…”
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On nonlinear variational inequalities by Muhammed Aslam Noor

“…The fixed point technique is used to prove the existence of a solution for a class of nonlinear variational inequalities related with odd order constrained boundary value problems and to suggest an iterative algorithm to compute the approximate solution.…”
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Integral BVPs for a Class of First-Order Impulsive Functional Differential Equations by Xiaofei He, Jingli Xie, Guoping Chen, Jianhua Shen

“…The methods of lower and upper solutions and monotone iterative technique are employed to the study of integral boundary value problems for a class of first-order impulsive functional differential equations. …”
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The solution of a singular integral equation with some applications in potential theory by N. T. Shawagfeh

“…An analytical solution is derived for a singular integral equation which governs some twodimensional potential boundary value problems in a region exterior to n-infinite co-axial circular strips. …”
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Hartman-Type and Lyapunov-Type Inequalities for a Fractional Differential Equation with Fractional Boundary Conditions by Imed Bachar, Hassan Eltayeb

“…We prove Hartman-type and Lyapunov-type inequalities for a class of Riemann–Liouville fractional boundary value problems with fractional boundary conditions. …”
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Error estimates for the finite element solutions of variational inequalities by M. Aslam Noor

“…For piecewise linear approximation of variational inequalities associated with the mildly nonlinear elliptic boundary value problems having auxiliary constraint conditions, we prove that the error estimate for u−uh in the W1,2-norm is of order h.…”
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Existence of Solutions for Fractional Differential Equations with p-Laplacian Operator and Integral Boundary Conditions by Jingli Xie, Lijing Duan

“…In this paper, we investigate a class of integral boundary value problems of fractional differential equations with a p-Laplacian operator. …”
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