Melting ternary hybrid nanofluid stagnation point flow with velocity slip past a stretching/shrinking sheet: Numerical simulation and validation via P2SATRA by Nur Syahirah Wahid, Nur Ezlin Zamri, Siti Zulaikha Mohd Jamaludin, Nur Hazirah Adilla Norzawary, Mohd Shareduwan Mohd Kasihmuddin, Mohd. Asyraf Mansor, Norihan Md Arifin, Ioan Pop

“…The governing partial differential equations (PDEs) are initially formulated and subsequently reduced to ordinary differential equations (ODEs). …”
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Machine learning-driven analysis of heat transfer in chemically reactive fluid flow considering Soret-Dufour effects by Shazia Habib, Saleem Nasir, Zeeshan Khan, Abdallah S. Berrouk, Waseem, Saeed Islam

“…By transforming the governing system of nonlinear partial differential equations into ordinary differential equations via similarity transformation, the methodology attains computational efficiency and solution precision. …”
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Existence and H-U Stability of Solution for Coupled System of Fractional-Order with Integral Conditions Involving Caputo-Hadamard Derivatives, Hadamard Integrals by Muath Awadalla, Muthaian Subramanian, Murugesan Manigandan, Kinda Abuasbeh

“…In this article, the primary focus of our study is to investigate the existence, uniqueness, and Ulam-Hyers stability results for coupled fractional differential equations of the Caputo-Hadamard type that are supplemented with Hadamard integral boundary conditions. …”
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Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications by Jiang Zhu, Dongmei Liu

“…By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.…”
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Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach by Panos K. Palamides, Alex P. Palamides

“…We investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a (positive) Green's function, the obtained solution is still of definite sign. …”
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Local existence result of the single dopant diffusion including cluster reactions of high order by R. Bader, W. Merz

“…The model includes a nonlinear system of reaction-drift-diffusion equations, a nonlinear system of ordinary differential equations in Banach spaces, and a nonlinear elliptic equation for the electrochemical potential. …”
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An Analysis of the Cluster-Detecting Property of the BCM Neuron by Lawrence Udeigwe

“…By exploring the qualitative behaviors of an underlying system of differential equations, we present a rigorous mathematical analysis of this cluster-detecting property. …”
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Existence of Two Positive Solutions for Two Kinds of Fractional p-Laplacian Equations by Yong Wu, Said Taarabti

“…The aim of this paper is to investigate the existence of two positive solutions to subcritical and critical fractional integro-differential equations driven by a nonlocal operator LKp. …”
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Nonstationary Fronts in the Singularly Perturbed Power-Society Model by M. G. Dmitriev, A. A. Pavlov, A. P. Petrov

“…The theory of contrasting structures in singularly perturbed boundary problems for nonlinear parabolic partial differential equations is applied to the research of formation of steady state distributions of power within the nonlinear “power-society” model. …”
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Approximate Solutions of Fractional Riccati Equations Using the Adomian Decomposition Method by Fei Wu, Lan-Lan Huang

“…In this paper, it was used to solve some fractional nonlinear differential equations.…”
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Superposed Incremental Deformations of an Elastic Solid Reinforced with Fibers Resistant to Extension and Flexure by Chun IL Kim

“…In particular, the complete systems of differential equations are obtained for the cases of Neo-Hookean and Mooney–Rivlin types of materials from which analytical solutions can be obtained.…”
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W2,p-Solvability of the Dirichlet Problem for Elliptic Equations with Singular Data by Loredana Caso, Roberta D’Ambrosio, Maria Transirico

“…We give an overview on some results concerning the unique solvability of the Dirichlet problem in W2,p, p>1, for second-order linear elliptic partial differential equations in nondivergence form and with singular data in weighted Sobolev spaces. …”
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Derivation of Equations for Flexible Multibody Systems in Terms of Quasi-Coordinates from the Extended Hamilton’s Principle by L. Meirovitch

“…In this article, hybrid (ordinary and partial) differential equations for flexible multibody systems are derived in terms of quasi-coordinates directly from the extended Hamilton's principle. …”
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Dynamical Modelling of Bone Formation and Resorption under Impulsive Estrogen Supplement: Effects of Parathyroid Hormone and Prolactin by Supassorn Aekthong, Chontita Rattanakul

“…A system of impulsive differential equations is developed in this paper in order to investigate the effects of parathyroid hormone and prolactin on bone-forming cells, namely, osteoblasts, and bone-resorbing cells, namely, osteoclasts, under the impulsive estrogen supplement. …”
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Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator by Burkhan T. Kalimbetov, Marat A. Temirbekov, Zhanibek O. Khabibullayev

“…The main idea of this method is based on the analysis of dual singular points of investigated equations and passage in the space of the larger dimension, what reduces to study of systems of first-order partial differential equations with incomplete initial data.…”
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Representation of a Solution of the Cauchy Problem for an Oscillating System with Multiple Delays and Pairwise Permutable Matrices by Josef Diblík, Michal Fečkan, Michal Pospíšil

“…Nonhomogeneous system of linear differential equations of second order with multiple different delays and pairwise permutable matrices defining the linear parts is considered. …”
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Pricing multi-asset financial derivatives with time-dependent parameters—Lie algebraic approach by C. F. Lo, C. H. Hui

“…Exploiting the dynamical symmetry of the pricing partial differential equations of the financial derivatives, the new method enables us to derive analytical closed-form pricing formulae very straightforwardly. …”
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Maximal regular boundary value problems in Banach-valued function spaces and applications by Veli B. Shakhmurov

“…In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value problems for parabolic equations, and their systems on cylindrical domain are studied.…”
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Error Analysis of Galerkin's Method for Semilinear Equations by Tadashi Kawanago

“…Some of our results may be applicable for investigating the quality of numerical verification methods for solutions of ordinary and partial differential equations.…”
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Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation by Hassan Eltayeb, Said Mesloub

“…It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. …”
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