Lie Symmetry Analysis for the General Classes of Generalized Modified Kuramoto-Sivashinsky Equation by Rong Qi, Muhammad Mobeen Munir, Nazish Younas, Muhammad Idrees, Jia-Bao Liu

“…Lie symmetry analysis of differential equations proves to be a powerful tool to solve or at least reduce the order and nonlinearity of the equation. …”
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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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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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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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Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes by Matteo Strozzi, Francesco Pellicano

“…The Rayleigh–Ritz method is applied to approximate linear eigenfunctions of the partial differential equations that govern the shell dynamics. An energy approach, based on Lagrange equations and series expansion of the displacements, is considered to reduce the initial partial differential equations to a set of nonlinear ordinary differential equations of motion. …”
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Integral Representation of Functions of Bounded Variation by Z. Lipcsey, I. M. Esuabana, J. A. Ugboh, I. O. Isaac

“…With Bainov’s introduction of impulsive differential equations having solutions of bounded variation, this class of functions had eventually entered into the theory of differential equations. …”
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A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators by Yassin Belkourchia, Lahcen Azrar

“…Thanks to this regularization, the resulting differential equations can be directly discretized using the DQM. …”
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Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries by Bermúdez, Alfredo, Padín, Iago

“…For this purpose, advantage is taken from the fact that optimal control problems for stochastic ordinary differential equations (SDE) can be equivalently formulated as optimal control problems for deterministic partial differential equations (PDE), namely, the corresponding Fokker–Planck equation.…”
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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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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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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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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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Lie and Riccati Linearization of a Class of Liénard Type Equations by A. G. Johnpillai, C. M. Khalique, F. M. Mahomed

“…The linearizing transformations are used to transform the underlying class of equations to linear third- and second-order ordinary differential equations, respectively. The general solution of this class of equations can then easily be obtained by integrating the linearized equations resulting from both of the linearization approaches. …”
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A new finite difference algorithm for boundary value problems involving transmission conditions by Semih Çavuşoğlu, Oktay Sh. Mukhtarov

“…The finite difference method (FDM) is used to find an approximate solution to ordinary and partial differential equations of various type using finite difference equations to approximate derivatives. …”
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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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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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DC Glow Discharge in Axial Magnetic Field at Low Pressures by Shen Gao, Shixiu Chen, Zengchao Ji, Wei Tian, Jun Chen

“…Results obtained from the model reveal that although the differential equations under the condition of axial magnetic field are consistent with the differential equations without considering the magnetic field, the solution of the equations is not completely consistent. …”
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Evaluating a family of two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence by R. Bonciani, V. Del Duca, H. Frellesvig, J.M. Henn, M. Hidding, L. Maestri, F. Moriello, G. Salvatori, V.A. Smirnov

“…The computation of the integrals is performed with the method of differential equations. We provide a choice of basis for the polylogarithmic sectors, that puts the system of differential equations in canonical form. …”
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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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