Almost Automorphic Mild Solutions to Neutral Parabolic Nonautonomous Evolution Equations with Nondense Domain by Zhanrong Hu, Zhen Jin

“…A unified framework is set up to investigate the existence and uniqueness of almost automorphic mild solutions to some classes of parabolic partial differential equations and neutral functional differential equations.…”
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Global Stability for Fractional Diffusion Equations in Biological Systems by Khalid Hattaf, Noura Yousfi

“…This paper proposes a new method of construction of Lyapunov functionals for the dynamical systems described by fractional differential equations and fractional partial differential equations. …”
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A First Application of the Backward Technique in Social Sciences: Exploring Demographic Noise in a Model with Three Personality Types by Roberto Macrelli, Margherita Carletti, Vincenzo Fano

“…Moving forward again from a continuous stochastic framework, we get to the continuous deterministic setting described by ordinary differential equations if we assume that noise can be neglected. …”
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Infinite Horizon Optimal Control of Stochastic Delay Evolution Equations in Hilbert Spaces by Xueping Zhu, Jianjun Zhou

“…An optimal control problem of stochastic delay partial differential equations is also given as an example to illustrate our results.…”
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Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time Scales by Jiang Zhu, Ying Zhu

“…Also the explicit solutions to homogeneous fractional Δ-differential equations and nonhomogeneous fractional Δ-differential equations are derived by using Laplace transform method.…”
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Linearization: Geometric, Complex, and Conditional by Asghar Qadir

“…Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of) differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. …”
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Lie Group Method of the Diffusion Equations by Jian-Qiang Sun, Rong-Fang Huang, Xiao-Yan Gu, Ling Yu

“…The diffusion equation is discretized in spacial direction and transformed into the ordinary differential equations. The ordinary differential equations are solved by Lie group method and the explicit Runge-Kutta method. …”
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The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations by Abdon Atangana, Adem Kılıçman

“…We make use of the properties of the Sumudu transform to solve nonlinear fractional partial differential equations describing heat-like equation with variable coefficients. …”
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Investigation of Two-Dimensional Viscoelastic Fluid with Nonuniform Heat Generation over Permeable Stretching Sheet with Slip Condition by Haroon Ur Rasheed, Zeeshan Khan, Saeed Islam, Ilyas Khan, Juan L. G. Guirao, Waris Khan

“…Here, in this research article, we have investigated an incompressible viscoelastic fluid flow over a uniform stretching surface sheet along with slip boundary conditions in the presence of porous media. The partial differential equations which govern the fluid flow are changed into ordinary differential equations through suitable similarity transformation variables. …”
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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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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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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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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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Asymptotic Comparison of the Solutions of Linear Time-Delay Systems with Point and Distributed Lags with Those of Their Limiting Equations by M. De la Sen

“…This paper investigates the relations between the particular eigensolutions of a limiting functional differential equation of any order, which is the nominal (unperturbed) linear autonomous differential equations, and the associate ones of the corresponding perturbed functional differential equation. …”
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Homotopy Perturbation Method for Thin Film Flow and Heat Transfer over an Unsteady Stretching Sheet with Internal Heating and Variable Heat Flux by I-Chung Liu, Ahmed M. Megahed

“…Similarity transformations are used to transform the governing equations to a set of coupled nonlinear ordinary differential equations. The obtained differential equations are solved approximately by the homotopy perturbation method (HPM). …”
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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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Linearization from Complex Lie Point Transformations by Sajid Ali, M. Safdar, Asghar Qadir

“…Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension d, with d≤4. …”
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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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