Gyrotatic dynamics of magneto viscoelastic material with thermal and solutal transport by Muhammad, Masood Khan, A.S. Alqahtani, M.Y. Malik

“…The controlling model of the governing equations is converted from partial differential equations into dimensionless form in terms of ordinary differential equations by using the similarity transformations approach. …”
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A Two-Fluid Conditional Averaging Paradigm for the Theory and Modeling of Turbulent Premixed Combustion by Vladimir L. Zimont

“…These equations are necessary for the development of model differential equations for the Reynolds stresses and the chemical source in the advanced modeling and simulation of turbulent premixed combustion. …”
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Mathematical modeling in autoimmune diseases: from theory to clinical application by Yaroslav Ugolkov, Yaroslav Ugolkov, Yaroslav Ugolkov, Antonina Nikitich, Antonina Nikitich, Cristina Leon, Gabriel Helmlinger, Kirill Peskov, Kirill Peskov, Kirill Peskov, Kirill Peskov, Victor Sokolov, Victor Sokolov, Alina Volkova, Alina Volkova

“…. ≥70% of the models were developed as nonlinear systems of ordinary differential equations, others – as partial differential equations, integro-differential equations, Boolean networks, or probabilistic models. …”
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Comment on “Variational Iteration Method for Fractional Calculus Using He’s Polynomials” by Ji-Huan He

“…A standard variational iteration algorithm for fractional differential equations is suggested.…”
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New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations by Mohamed S. Al-luhaibi

“…Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.…”
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On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space by Hamdy M. Ahmed

“…We also give an application for stochastic integropartial differential equations of fractional order.…”
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An Lp-Estimate for Weak Solutions of Elliptic Equations by Sara Monsurrò, Maria Transirico

“…We prove an Lp-a priori bound, p>2, for solutions of second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains.…”
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Space-time caustics by Arthur D. Gorman

“…The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of linear differential equations modelling wave propagation in spatially inhomogeneous media at caustic (turning) points. …”
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Approximate Analytical Solutions of the Fractional-Order Brusselator System Using the Polynomial Least Squares Method by Constantin Bota, Bogdan Căruntu

“…PLSM allows us to compute approximate analytical solutions for the Brusselator system, which is a fractional-order system of nonlinear differential equations.…”
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Stability of Impulsive Differential Systems by Andrejs Reinfelds, Lelde Sermone

“…The asymptotic phase property and reduction principle for stability of a trivial solution is generalized to the case of the noninvertible impulsive differential equations in Banach spaces whose linear parts split into two parts and satisfy the condition of separation.…”
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The Hamiltonian Structure and Algebrogeometric Solution of a 1 + 1-Dimensional Coupled Equations by Hongfei Pan, Tiecheng Xia

“…A 1 + 1-dimensional coupled soliton equations are decomposed into two systems of ordinary differential equations. The Abel-Jacobi coordinates are introduced to straighten the flows, from which the algebrogeometric solutions of the coupled 1 + 1-dimensional equations are obtained in terms of the Riemann theta functions.…”
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Numerical Simulation and Symmetry Reduction of a Two-Component Reaction-Diffusion System by Jina Li, Xuehui Ji

“…In this paper, the symmetry classification and symmetry reduction of a two-component reaction-diffusion system are investigated, the reaction-diffusion system can be reduced to system of ordinary differential equations, and the solutions and numerical simulation will be showed by examples.…”
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On the existence of classical solutions for differential-functional IBVP by Krzysztof A. Topolski

“…Our formulation and results cover a large class of parabolic problems both with a deviated argument and integro-differential equations.…”
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Variable Step Size Adams Methods for BSDEs by Qiang Han

“…For backward stochastic differential equations (BSDEs), we construct variable step size Adams methods by means of Itô–Taylor expansion, and these schemes are nonlinear multistep schemes. …”
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Formulation and Solution of th-Order Derivative Fuzzy Integrodifferential Equation Using New Iterative Method with a Reliable Algorithm by A. A. Hemeda

“…The analysis is accompanied by numerical examples which confirm efficiency and power of this method in solving fuzzy integro-differential equations.…”
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Fixed Point Theorems of Superlinear Operators with Applications by Shaoyuan Xu, Yan Han

“…The results are applied to nonlinear integral equations and partial differential equations.…”
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Topological structure of solution sets of differential inclusions: the constrained case by Wojciech Kryszewski

“…We survey and announce some current results on the existence, the viability, and the topological structure of the viable solutions of differential equations and inclusion in Banach spaces under set constraints. …”
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A parallel algorithm for solving one problem of nonlinear optics by Raimondas Čiegis, Genė Kairytė, P. Ratė

“… This paper deals with a system of nonlinear differential equations, which describe the interaction of two focussed laser beams.The problem is approximated by a splitting finite difference scheme. …”
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A New Type of Distributed Parameter Control Systems: Two-Point Boundary Value Problems for Infinite-Dimensional Dynamical Systems by De-Xing Kong, Fa Wu

“…This survey note describes a new type of distributed parameter control systems—the two-point boundary value problems for infinite-dimensional dynamical systems, particularly, for hyperbolic systems of partial differential equations of second order, some of the discoveries that have been done about it and some unresolved questions.…”
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Degenerate Differential Operators with Parameters by Veli B. Shakhmurov

“…In applications, the nonlocal boundary value problems for degenerate elliptic partial differential equations and for systems of elliptic equations with parameters on cylindrical domain are studied.…”
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