Combined Effects of Thermal Radiation and Nanoparticles on Free Convection Flow and Heat Transfer of Casson Fluid over a Vertical Plate by M. G. Sobamowo

“…The governing systems of nonlinear partial differential equations of the flow and heat transfer processes are converted to systems of nonlinear ordinary differential equations through similarity transformations. …”
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Generalized Exponential Trichotomies for Abstract Evolution Operators on the Real Line by Nicolae Lupa, Mihail Megan

“…We emphasize that we do not assume the invertibility of the evolution operators on the whole space X (unlike the case of evolution operators generated by differential equations).…”
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VIM for Solving the Pollution Problem of a System of Lakes by J. Biazar, M. Shahbala, H. Ebrahimi

“…Monitoring pollution is the first step toward planning to save the environment. The use of differential equations of monitoring pollution has become possible. …”
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Dynamical Behavior of a Predator-Prey System Incorporating a Prey Refuge with Impulse Effect by Zuxiong Li, Xue Yang, Shengnan Fu

“…Further, by applying the bifurcation theory of impulsive differential equations, conditions under which the system has a positive periodic solution are obtained. …”
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Rough Paths above Weierstrass Functions by Cellarosi, Francesco, Selk, Zachary

“…Rough paths theory allows for a pathwise theory of solutions to differential equations driven by highly irregular signals. …”
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Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations by A. V. Krysko, Jan Awrejcewicz, Irina V. Papkova, Olga Szymanowska, V. A. Krysko

“…Solutions to linear and nonlinear differential equations are found using the principal component analysis (PCA).…”
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Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications by Jürgen Geiser

“…We concentrate on a linearised integral part and a reformulation to a system of first order differential equations. Such modifications allow for applying standard iterative splitting schemes and for extending the schemes, respecting the integral operator. …”
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New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs by Norazak Senu, Mohamed Suleiman, Fudziah Ismail, Norihan Md Arifin

“…These new methods are more efficient when compared with current methods of similar type and with the L-stable Runge-Kutta pair derived by Butcher and Chen (2000) for the numerical integration of second-order differential equations with periodic solutions.…”
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Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation by Andrew Gratien Johnpillai, Chaudry Masood Khalique

“…These subalgebras are then used to reduce the underlying equation to nonlinear third-order ordinary differential equations. Exact traveling wave group-invariant solutions for the equation are constructed by integrating the reduced ordinary differential equations. …”
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Notes on almost-periodicity in topological vector spaces by Gaston Mandata N'guérékata

“…A study is made of almost-periodic functions in topological vector spaces with applications to abstract differential equations.…”
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Finite eigenfuction approximations for continuous spectrum operators by Robert M. Kauffman

“…The theory is designed for application to ordinary and partial differential equations; relationships between the abstract theory and differential equations are worked out in the paper. …”
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Exact Solutions for Unsteady Free Convection Flow of Casson Fluid over an Oscillating Vertical Plate with Constant Wall Temperature by Asma Khalid, Ilyas Khan, Sharidan Shafie

“…The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. …”
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An Exact Solution of the Binary Singular Problem by Baiqing Sun, Kun Tang, Hongmei Zhang, Shan Xiong

“…Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. …”
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Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps by Guodong Liu, Xiaohong Wang, Xinzhu Meng, Shujing Gao

“…Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). …”
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Approximate Solutions of Fisher's Type Equations with Variable Coefficients by A. H. Bhrawy, M. A. Alghamdi

“…Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations.…”
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Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps by Tingting Ma, Xinzhu Meng, Zhengbo Chang

“…Using the comparison theorem of stochastic differential equations and asymptotic approaches, sufficient conditions for persistence in mean and extinction of three species are derived. …”
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Further Developments of Bessel Functions via Conformable Calculus with Applications by Mahmoud Abul-Ez, Mohra Zayed, Ali Youssef

“…The theory of Bessel functions is a rich subject due to its essential role in providing solutions for differential equations associated with many applications. …”
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Thermo-Magneto-Solutal Squeezing Flow of Nanofluid between Two Parallel Disks Embedded in a Porous Medium: Effects of Nanoparticle Geometry, Slip and Temperature Jump Conditions by M. G. Sobamowo, A. T. Akinshilo, A. A. Yinusa

“…Similarity variables are used to transform the developed governing systems of nonlinear partial differential equations to systems of nonlinear ordinary differential equations. …”
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Multiple Slip Effects on MHD Unsteady Flow Heat and Mass Transfer Impinging on Permeable Stretching Sheet with Radiation by Fazle Mabood, Stanford Shateyi

“…Suitable similarity variables are used to transform governing partial differential equations into a system of coupled nonlinear ordinary differential equations. …”
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A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme by Azmy S. Ackleh, Mark L. Delcambre, Karyn L. Sutton, Don G. Ennis

“…The model consists of a system of nonlinear hyperbolic partial differential equations coupled with three nonlinear ordinary differential equations. …”
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