Alternative models for cyclic lemming dynamics by Hao Wang, Yang Kuang

“…Many natural population growths and interactions are affected byseasonal changes, suggesting that these natural population dynamicsshould be modeled by nonautonomous differential equations instead ofautonomous differential equations. …”
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Applications of Karry-Kalim-Adnan Transformation (KKAT) to Mechanics and Electrical Circuits by Karry Iqbal, Muhammad Kalim, Adnan Khan

“…In this paper, we have used the new integral transformation known as Karry-Kalim-Adnan transformation (KKAT) to solve the ordinary linear differential equations as well as partial differential equations. …”
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Fractional-View Analysis of Space-Time Fractional Fokker-Planck Equations within Caputo Operator by Saleh Alshammari, Naveed Iqbal, Mohammad Yar

“…The convergent series form solution demonstrates the method’s efficiency in resolving several types of fractional differential equations. Compared to other methods of finding approximate and exact solutions for nonlinear partial differential equations, this technique is more efficient and time-consuming.…”
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A Note on Impulsive Fractional Evolution Equations with Nondense Domain by Zufeng Zhang, Bin Liu

“…This paper is concerned with the existence of integral solutions for nondensely defined fractional functional differential equations with impulse effects. Some errors in the existing paper concerned with nondensely defined fractional differential equations are pointed out, and correct formula of integral solutions is established by using integrated semigroup and some probability densities. …”
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Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps by Wei Mao, Xuerong Mao

“…We investigate a class of stochastic pantograph differential equations with Markovian switching and Levy jumps. …”
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Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition by Habtamu Garoma Debela

“…This paper presents the study of singularly perturbed differential equations of convection-diffusion type with nonlocal boundary condition. …”
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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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Asymptotic Methods for Solitary Solutions and Compactons by Ji-Huan He

“…This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. …”
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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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