Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators by Chen Yang, Xiaolin Zhu

“…This paper considers a system of fractional differential equations involving p-Laplacian operators and two parameters D0+α1φp1D0+β1ut+λft,ut,vt=0,0<t<1,D0+α2φp2D0+β2vt+μgt,ut,vt=0,0<t<1,u0=u1=u′0=u′1=0,D0+β1u0=0,D0+β1u1=b1D0+β1uη1,v0=v1=v′0=v′1=0,D0+β2v0=0,D0+β2v1=b2D0+β2vη2, where αi∈1,2, βi∈3,4, D0+αi and D0+βi are the standard Riemann-Liouville derivatives, φpis=spi−2s,pi>1, φpi−1=φqi, 1/pi+1/qi=1,ηi∈0,1,bi∈0,ηi1−αi/pi−1, i=1,2, and f,g∈C0,1×0,+∞×0,+∞,0,+∞ and λ and μ are two positive parameters. …”
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FEATURES OF ELECTROMECHANICAL ACOUSTIC ENERGY CONVERSION BY CYLINDRICAL PIEZOCERAMIC TRANSDUCERS WITH INTERNAL SCREENS IN COMPOSITION OF FLAT SYSTEMS by A. G. Leiko, I. V. Kandrachuk, A. O. Sviatnenko

“…The physical fields arising from the emission of sound by such a system are determined by the joint solution of the system of differential equations: the wave equation; equations of motion of thin piezoceramic shells with circular polarization in displacements; the equations of forced electrostatics for piezoceramics at given boundary conditions, the conditions of conjugation of fields at the boundaries of the division of domains and electric conditions.The solution of the problem is reduced to the solution of an infinite system of linear algebraic equations with respect to unknown coefficients of field expansions.An analysis of the results of numerical calculations, performed on the basis of the obtained analytical relations, called to establish a number of features in the electromechanical acoustic transformation of energy by emitters in the composition of flat systems. …”
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MOVIMENTO BROWNIANO: APLICAÇÃO EM ESTRATÉGIAS DE BUSCA by Matheus Dias Carvalho, Ricardo de Carvalho Falcão, Antonio Marcos de Oliveira Siqueira

“…This paper structured partial differential equations governing this process for the immortal case of walker, and later found analytical solutions to these expressions. …”
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Analysis of a Two-Phase MHD Free Convection Generalized Water–Ethylene Glycol (50 : 50) Dusty Brinkman-Type Nanofluid Pass through Microchannel by Dolat Khan, Musawa Yahya Almusawa, Waleed Hamali, M. Ali Akbar

“…While the left plate moves at a consistent velocity and the right plate stays stationary, the fluid is also evenly dispersed with all dust particles that have a spherical form. Partial differential equations (PDE) are used to present the mathematical modeling. …”
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Stochastic Diffusive Modeling of CO₂ Emissions with Population and Energy Dynamics by Muhammad Shoaib Arif, Kamaleldin Abodayeh, Hisham M. Al-Khawar, Yasir Nawaz

“…A novel numerical scheme, an extension of the Euler-Maruyama algorithm, is proposed to solve stochastic time-dependent partial differential equations governing the model. The scheme's consistency and stability are rigorously analyzed in the mean square sense. …”
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CALCULATION OF STATIC PARAMETERS OF SILICON DIODE CONTAINING δ-LAYER OF TRIPLE-CHARGED POINT DEFECTS IN SYMMETRIC p–n-JUNCTION by N. A. Poklonski, A. I. Kovalev, N. I. Gorbachuk, S. V. Shpakovski

“…It was assumed that the cross-section for v-band hole capture on t-defects is greater than the cross-section for c-band electron capture on t-defects.The system of stationary nonlinear differential equations, which describe in the drift-diffusion approximation a migration of electrons and holes in semiconductors, is solved numerically. …”
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Accelerating and decelerating flow of radiatively Casson fluid between two permeable disks under convective boundary conditions by A. Naeem, Z. Abbas, M.Y. Rafiq

“…Jacobi elliptic sine square function is used to derive the solution of non-linear differential equations by transforming the equations into an elliptic integral form and then by using a change of variables which simplifies the governing equations so that the solution can be derived easily. …”
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Evidence of Exponential Speed-Up in the Solution of Hard Optimization Problems by Fabio L. Traversa, Pietro Cicotti, Forrest Sheldon, Massimiliano Di Ventra

“…Then, we solve its associated nonlinear ordinary differential equations numerically, towards the equilibrium points. …”
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Spatially Distributed Morphogen Production and Morphogen Gradient Formation by Arthur D. Lander, Qing Nie, Frederic Y. M. Wan

“…Partial differential equations and auxiliaryconditions governing the activities of the morphogen Dpp in Drosophila wingimaginal discs were formulated and analyzed as Systems B, R, and C in[7][9][10]. …”
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Mathematical Model and Characteristics of the Induction Motor with a Power Supply from a Current Source by V. S. Malyar, A. V. Malyar

“…The transients are described by the system of differential equations of electrical equilibrium of the transformed circuits of the motor and the equation of the rotor motion and the steady-state modes by the system of algebraic equation. …”
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On the Boundary Conditions in Out-of-Plane Analysis of Thin Plates by the Finite Point Method by Sadegh Tavakoliyan, Mohamad Najar, Parham Memarzadeh, Tadeh Zirakian

“…The finite point method (FPM) is a numerical, mesh-free technique for solving differential equations, particularly in fluid dynamics. While the FPM has been previously applied in solid mechanics to analyze plates under in-plane loading, there remains a notable scarcity of research exploring the out-of-plane analysis of elastic plates using this method. …”
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Entropy Analysis of Carreau Nanofluid Flow in the Presence of Joule Heating and Viscous Dissipation Past Unsteady Stretching Cylinder by Eshetu Haile Gorfie, Gizachew Bayou Zegeye, Gurju Awgichew Zergaw

“…The governing partial differential equations are transformed into first‐order initial value problems by similarity transformation and linearization. …”
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An Evolutionary Game Model of a Regional Logistics Service Supply Chain Complex Network in a Blockchain Environment by Guangsheng Zhang, Zhaomin Zhang

“…The stability theorem of differential equations is employed to elucidate the inherent decision-making mechanisms present in the game. …”
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A minimal mathematical model for the initial molecular interactions of death receptor signalling by Christian Winkel, Simon Neumann, Christina Surulescu, Peter Scheurich

“…We use here a mass action kinetics approach to establish an ordinary differential equations model describing the dynamics of primary ligand/receptor complex formation as a basis for further clustering on the cell membrane. …”
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The Effect of Delay Techniques on a Lassa Fever Epidemic Model by Ali Raza, Eugenio Rocha, Emad Fadhal, Rashid I. H. Ibrahim, Eman Afkar, Muhammad Bilal

“…By introducing a delay parameter and decay exponential term into the existing model in the literature, we got the system of highly nonlinear delay differential equations (DDEs). The fundamental properties such as positivity, boundedness, existence, and uniqueness are verified for the said model. …”
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BERT-Residual Quantum Language Model Inspired by ODE Multi-Step Method by Shaohui Liang, Yingkui Wang, Shuxin Chen

“…Therefore, in this paper, we propose the BERT-Residual quantum language model inspired by the multi-step method of ordinary differential equations (ODE), using the density matrix to capture the semantic high-order interaction features missing in the BERT modeling process, and obtain the sentence representation, and perform the first step Residuals. …”
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Model analysis for an HIV infectious disease using elasticity and sensitivity techniques by Honar J. Hamad, Sarbaz H. A. Khoshnaw, Muhammad Shahzad

“…The model includes a class of nonlinear ordinary differential equations, and has both infection-free and endemic infection equilibrium points. …”
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SOLUTION OF THE PROBLEM OF OIL-POOL IN-SITU COMBUSTION FRONT PROPAGATION ON THE BASIS OF HEURISTIC HYPOTHESIS REGARDING TEMPERATURE AND CONCENTRATION PROFILES by K. V. Dobrego

“…Simple algebraic and differential equations fordetermination of the temperature and concentration profiles as well as for the front propagation velocity are derived for two cases i.e. the lack of oxidizer and the fuel component fault. …”
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A Graphical Approach for Hybrid Simulation of 3D Diffusion Bio-Models via Coloured Hybrid Petri Nets by Amr Ismail, Mostafa Herajy, Elsayed Atlam, Monika Heiner

“…The traditional approach to construct and simulate 3D models is to build a system of partial differential equations (PDEs). Although this approach may be computationally efficient and has been employed by many researchers over the years, it is not always intuitive since it does not provide a visual depiction of the modelled systems. …”
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A numerical framework for computing steady states of structured population models and their stability by Inom Mirzaev, David M. Bortz

“…In particular, we use the Trotter-Kato Theorem to approximate the infinitesimal generator of an evolution equation on a finite dimensional space, which in turn reduces the evolution equation into a system of ordinary differential equations. Consequently, we approximate and study the asymptotic behavior of stationary solutions. …”
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