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Artykuły w czasopismach na temat „Equation”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

Sriram, S., та P. Veeramallan. "On the Integer Solution of the Transcendental Equation √2𝑧−4=√𝑥+√𝐶𝑦± √𝑥−√𝐶𝑦". Indian Journal of Advanced Mathematics (IJAM) 2, № 1 (2022): 1–4. https://doi.org/10.54105/ijam.C1120.041322.

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<strong>Abstract:</strong> Let C be a positive non-square integer. In this paper, we look at the complete solutions of the Transcendental equation √𝟐𝒛−𝟒=√𝒙+√𝑪𝒚± √𝒙−√𝑪𝒚 , where 𝒙𝟐−𝑪𝒚𝟐=𝜶𝟐 or 𝟐𝟐𝒕. In addition, we find repeated relationships in the solutions to this figure.

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2

Karakostas, George L. "Asymptotic behavior of a certain functional equation via limiting equations." Czechoslovak Mathematical Journal 36, no. 2 (1986): 259–67. http://dx.doi.org/10.21136/cmj.1986.102089.

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3

Parkala, Naresh, and Upender Reddy Gujjula. "Mohand Transform for Solution of Integral Equations and Abel's Equation." International Journal of Science and Research (IJSR) 13, no. 5 (2024): 1188–91. http://dx.doi.org/10.21275/sr24512145111.

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4

Domoshnitsky, Alexander, and Roman Koplatadze. "On Asymptotic Behavior of Solutions of Generalized Emden-Fowler Differential Equations with Delay Argument." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/168425.

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The following differential equationu(n)(t)+p(t)|u(σ(t))|μ(t) sign u(σ(t))=0is considered. Herep∈Lloc(R+;R+), μ∈C(R+;(0,+∞)), σ∈C(R+;R+), σ(t)≤t, andlimt→+∞⁡σ(t)=+∞. We say that the equation is almost linear if the conditionlimt→+∞⁡μ(t)=1is fulfilled, while iflim⁡supt→+∞⁡μ(t)≠1orlim⁡inft→+∞⁡μ(t)≠1, then the equation is an essentially nonlinear differential equation. In the case of almost linear and essentially nonlinear differential equations with advanced argument, oscillatory properties have been extensively studied, but there are no results on delay equations of this sort. In this paper, new

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5

Zead, Yahya Ali Allawee. "Application New Iterative Method For Solving Nonlinear Burger's Equation And Coupled Burger's Equations." International Journal of Computer Science Issues 15, no. 3 (2018): 31–35. https://doi.org/10.5281/zenodo.1292414.

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In the recent research , the numerical solution of Nonlinear Burger’s equation and coupled Burger’s equation is obtained Nonlinear using a New Iterative Method (NIM) is being proposed to obtain. We have shown that the NIM solution is more accurate as compared to the techniques like, Burger’s equation and coupled Burger’s equation method and HPM method. more, results also demonstrate that NIM solution is more reliable, easy to compute and computationally fast as compared to HPM method.

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6

Becker, Leigh, Theodore Burton, and Ioannis Purnaras. "Complementary equations: a fractional differential equation and a Volterra integral equation." Electronic Journal of Qualitative Theory of Differential Equations, no. 12 (2015): 1–24. http://dx.doi.org/10.14232/ejqtde.2015.1.12.

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7

Zhao, Wenling, Hongkui Li, Xueting Liu, and Fuyi Xu. "Necessary and Sufficient Conditions for the Existence of a Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations." Mathematical Problems in Engineering 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/672695.

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We study the Hermitian positive definite solutions of the nonlinear matrix equationX+A∗X−2A=I, whereAis ann×nnonsingular matrix. Some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation are given. However, based on the necessary and sufficient conditions, some properties and the equivalent equations ofX+A∗X−2A=Iare presented while the matrix equation has a Hermitian positive definite solution.

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8

Bobylev, Alexander Vasilievich, and Sergei Borisovitch Kuksin. "Boltzmann equation and wave kinetic equations." Keldysh Institute Preprints, no. 31 (2023): 1–20. http://dx.doi.org/10.20948/prepr-2023-31.

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The well-known nonlinear kinetic equations (in particular, the wave kinetic equation and the quantum Nordheim – Uehling – Uhlenbeck equations) are considered as a natural generalization of the classical spatially homogeneous Boltzmann equation. To this goal we introduce the generalized kinetic equation that depends on a function of four real variables F(x1; x2; x3; x4). The function F is assumed to satisfy certain commutation relations. The general properties of this equation are studied. It is shown that the above mentioned kinetic equations correspond to different forms of the function (poly

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9

N O, Onuoha. "Transformation of Parabolic Partial Differential Equations into Heat Equation Using Hopf Cole Transform." International Journal of Science and Research (IJSR) 12, no. 6 (2023): 1741–43. http://dx.doi.org/10.21275/sr23612082710.

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10

Prokhorova, M. F. "Factorization of the reaction-diffusion equation, the wave equation, and other equations." Proceedings of the Steklov Institute of Mathematics 287, S1 (2014): 156–66. http://dx.doi.org/10.1134/s0081543814090156.

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11

Yan, Zhenya. "Complex PT -symmetric nonlinear Schrödinger equation and Burgers equation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (2013): 20120059. http://dx.doi.org/10.1098/rsta.2012.0059.

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The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg–de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report on exact solutions of one- and two-dimensional nonlinear Schrödinger equations (known as the Gross–Pitaevskii equation in Bose–Einstein condensates) with several complex -symmetric potentials. Finally,

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12

Shi, Yong-Guo, and Xiao-Bing Gong. "Linear functional equations involving Babbage’s equation." Elemente der Mathematik 69, no. 4 (2014): 195–204. http://dx.doi.org/10.4171/em/263.

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13

Mickens, Ronald E. "Difference equation models of differential equations." Mathematical and Computer Modelling 11 (1988): 528–30. http://dx.doi.org/10.1016/0895-7177(88)90549-3.

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14

Cohen, Leon. "Phase-space equation for wave equations." Journal of the Acoustical Society of America 133, no. 5 (2013): 3435. http://dx.doi.org/10.1121/1.4806061.

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15

Svinin, Andrei K. "Somos-4 equation and related equations." Advances in Applied Mathematics 153 (February 2024): 102609. http://dx.doi.org/10.1016/j.aam.2023.102609.

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16

Čermák, Jan, and Petr Kundrát. "Linear differential equations with unbounded delays and a forcing term." Abstract and Applied Analysis 2004, no. 4 (2004): 337–45. http://dx.doi.org/10.1155/s1085337504306020.

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The paper discusses the asymptotic behaviour of all solutions of the differential equationy˙(t)=−a(t)y(t)+∑i=1nbi(t)y(τi(t))+f(t),t∈I=[t0,∞), with a positive continuous functiona, continuous functionsbi,f, andncontinuously differentiable unbounded lags. We establish conditions under which any solutionyof this equation can be estimated by means of a solution of an auxiliary functional equation with one unbounded lag. Moreover, some related questions concerning functional equations are discussed as well.

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17

Bose, A. K. "An integral equation associated with linear homogeneous differential equations." International Journal of Mathematics and Mathematical Sciences 9, no. 2 (1986): 405–8. http://dx.doi.org/10.1155/s0161171286000509.

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Associated with each linear homogeneous differential equationy(n)=∑i=0n−1ai(x)y(i)of ordernon the real line, there is an equivalent integral equationf(x)=f(x0)+∫x0xh(u)du+∫x0x[∫x0uGn−1(u,v)a0(v)f(v)dv]duwhich is satisfied by each solutionf(x)of the differential equation.

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18

Gupta, Rohit, Rakesh Kumar Verma, and Sanjay Kumar Verma. "Solving Wave Equation and Heat Equation by Rohit Transform (RT)." Journal of Physics: Conference Series 2325, no. 1 (2022): 012036. http://dx.doi.org/10.1088/1742-6596/2325/1/012036.

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Abstract The wave equation and the heat equation are widely known differential equations coming to light in engineering, basic and material sciences. The differential equations which represent the wave equation and the heat equation are usually solved by the exact technique or by the approximate technique or by the purely numerical technique. Since the implementation of these techniques is very complex, computationally vigorous, and requires elaborate computations, therefore, for finding the solutions of differential equations depicting the wave equation and the heat equation, there is a need

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19

Sinkala, Winter, and Tembinkosi F. Nkalashe. "Studying a Tumor Growth Partial Differential Equation via the Black–Scholes Equation." Computation 8, no. 2 (2020): 57. http://dx.doi.org/10.3390/computation8020057.

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Two equations are considered in this paper—the Black–Scholes equation and an equation that models the spatial dynamics of a brain tumor under some treatment regime. We shall call the latter equation the tumor equation. The Black–Scholes and tumor equations are partial differential equations that arise in very different contexts. The tumor equation is used to model propagation of brain tumor, while the Black–Scholes equation arises in financial mathematics as a model for the fair price of a European option and other related derivatives. We use Lie symmetry analysis to establish a mapping betwee

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20

Chu, Yu-Ming, Shumaila Javeed, Dumitru Baleanu, Sidra Riaz, and Hadi Rezazadeh. "New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation." Advances in Mathematical Physics 2020 (November 5, 2020): 1–14. http://dx.doi.org/10.1155/2020/5098329.

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This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). The suggested technique is implemented to obtain the solutions of space-time Kolmogorov Petrovskii Piskunov (KPP) equation and its derived equations, namely, Fitzhugh Nagumo (FHN) equation and Newell-Whitehead (NW) equation. The considered models are significant in biology. The KPP equation describes genetic model for spread of dominant gene through population. The FHN equation is imperative in the study of in

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21

Abdillah, Muhammad Taufik, Berlian Setiawaty, and Sugi Guritman. "The Solution of Generalization of the First and Second Kind of Abel’s Integral Equation." JTAM (Jurnal Teori dan Aplikasi Matematika) 7, no. 3 (2023): 631. http://dx.doi.org/10.31764/jtam.v7i3.14193.

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Integral equations are equations in which the unknown function is found to be inside the integral sign. N. H. Abel used the integral equation to analyze the relationship between kinetic energy and potential energy in a falling object, expressed by two integral equations. This integral equation is called Abel's integral equation. Furthermore, these equations are developed to produce generalizations and further generalizations for each equation. This study aims to explain generalizations of the first and second kind of Abel’s integral equations, and to find solution for each equation. The method

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22

Nikolova, Elena V. "Exact Travelling-Wave Solutions of the Extended Fifth-Order Korteweg–de Vries Equation via Simple Equations Method (SEsM): The Case of Two Simple Equations." Entropy 24, no. 9 (2022): 1288. http://dx.doi.org/10.3390/e24091288.

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We apply the Simple Equations Method (SEsM) for obtaining exact travelling-wave solutions of the extended fifth-order Korteweg–deVries (KdV) equation. We present the solution of this equation as a composite function of two functions of two independent variables. The two composing functions are constructed as finite series of the solutions of two simple equations. For our convenience, we express these solutions by special functions V, which are solutions of appropriate ordinary differential equations, containing polynomial non-linearity. Various specific cases of the use of the special function

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23

Mohamad- Jawad, Anwar. "The Sine-Cosine Function Method for Exact Solutions of Nonlinear Partial Differential Equations." Journal of Al-Rafidain University College For Sciences ( Print ISSN: 1681-6870 ,Online ISSN: 2790-2293 ), no. 2 (October 17, 2021): 120–39. http://dx.doi.org/10.55562/jrucs.v32i2.327.

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The Sine-Cosine function algorithm is applied for solving nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of nonlinear partial differential equations such as, The K(n + 1, n + 1) equation, Schrödinger-Hirota equation, Gardner equation, the modified KdV equation, perturbed Burgers equation, general Burger’s-Fisher equation, and Cubic modified Boussinesq equation which are the important Soliton equations.Keywords: Nonlinear PDEs, Exact Solutions, Nonlinear Waves, Gardner equation, Sine-Cosine function method, The Schrödinger-Hirota e

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24

Wang, Haifeng, and Yufeng Zhang. "Self-Adjointness and Conservation Laws of Frobenius Type Equations." Symmetry 12, no. 12 (2020): 1987. http://dx.doi.org/10.3390/sym12121987.

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The Frobenius KDV equation and the Frobenius KP equation are introduced, and the Frobenius Kompaneets equation, Frobenius Burgers equation and Frobenius Harry Dym equation are constructed by taking values in a commutative subalgebra Z2ε in the paper. The five equations are selected as examples to help us study the self-adjointness of Frobenius type equations, and we show that the first two equations are quasi self-adjoint and the last three equations are nonlinear self-adjointness. It follows that we give the symmetries of the Frobenius KDV and the Frobenius KP equation in order to construct t

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25

Ndogmo, Jean-Claude, and Fazal Mahomed. "On certain properties of linear iterative equations." Open Mathematics 12, no. 4 (2014): 648–57. http://dx.doi.org/10.2478/s11533-013-0364-z.

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Abstract An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained, and this gives rise to the derivation of important symmetry properties for iterati

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26

Naher, Hasibun, and Farah Aini Abdullah. "New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the(2+1)-Dimensional Evolution Equation." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/486458.

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The generalized Riccati equation mapping is extended with the basic(G′/G)-expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the (2+1)-dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equationG′(η)=w+uG(η)+vG2(η)is executed with arbitrary constant coefficients and called the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbo

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27

Hino, Yoshiyuki, and Taro Yoshizawa. "Total stability property in limiting equations for a functional-differential equation with infinite delay." Časopis pro pěstování matematiky 111, no. 1 (1986): 62–69. http://dx.doi.org/10.21136/cpm.1986.118265.

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28

Bozdoğan, Abdürrezzak Emin. "Length Contraction, Time Dilation, Mass, Momentum and Energy Equations, Particle and Antiparticle Potential Energy, Pair Production and Annihilation Energy Equations from Harmonic Oscillator Rest Energy Equation and New Relations from Uncertainty Principle." European Journal of Applied Physics 7, no. 1 (2025): 1–8. https://doi.org/10.24018/ejphysics.2025.7.1.352.

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The harmonic oscillator total rest energy equation is derived from simple and quantum-mechanical harmonic oscillator equations. Length contraction, time dilation, relativistic mass, momentum, and energy equations for a particle, electron, and Planck particle are derived from harmonic oscillator total rest energy equation and new relations derived from the Heisenberg uncertainty principle. Particle and antiparticle, electron and positron potential energy equations; particle-antiparticle, electron-positron pair productions, and pair annihilations minimum energy equations are derived from harmoni

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29

Chiang, Chun-Yueh. "A Note on the⊤-Stein Matrix Equation." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/824641.

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This note is concerned with the linear matrix equationX=AX⊤B + C, where the operator(·)⊤denotes the transpose (⊤) of a matrix. The first part of this paper sets forth the necessary and sufficient conditions for the unique solvability of the solutionX. The second part of this paper aims to provide a comprehensive treatment of the relationship between the theory of the generalized eigenvalue problem and the theory of the linear matrix equation. The final part of this paper starts with a brief review of numerical methods for solving the linear matrix equation. In relation to the computed methods,

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30

Kumar, Anil, and Gaurav Varshney. "IMPLEMENTATION AND ASSESSMENT OF THE SIMPLE EQUATION TECHNIQUE FOR SOLVING NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS." jnanabha 54, no. 01 (2024): 76–82. http://dx.doi.org/10.58250/jnanabha.2024.54109.

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In this paper, the simple equation method is especially used to solve two Nonlinear Partial Differential Partial Equations NLPDEs, the Kodomstev-Petviashvili (KP) equation and the (2+1)-dimensional breaking soliton equation. The modified Benjamin-Bona-Mahony equation and the Klein-Gordon equation in (1+2) dimensions are two illustrations of second order nonlinear equations that can benefit from using this approach. The Bernoulli equation acts as the trial condition and aids in the mathematical a description of the nonlinear wave equation in the simple equation.

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31

Delgado-Vences, Francisco, and Franco Flandoli. "A spectral-based numerical method for Kolmogorov equations in Hilbert spaces." Infinite Dimensional Analysis, Quantum Probability and Related Topics 19, no. 03 (2016): 1650020. http://dx.doi.org/10.1142/s021902571650020x.

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We propose a numerical solution for the solution of the Fokker–Planck–Kolmogorov (FPK) equations associated with stochastic partial differential equations in Hilbert spaces. The method is based on the spectral decomposition of the Ornstein–Uhlenbeck semigroup associated to the Kolmogorov equation. This allows us to write the solution of the Kolmogorov equation as a deterministic version of the Wiener–Chaos Expansion. By using this expansion we reformulate the Kolmogorov equation as an infinite system of ordinary differential equations, and by truncating it we set a linear finite system of diff

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32

ZHANG, YUFENG, HONWAH TAM, and JING ZHAO. "GENERALIZED mKdV EQUATION, LIOUVILLE EQUATION, SINE-GORDON EQUATION AND SINH-GORDON EQUATION AS WELL AS A FORMAL BÄCKLUND TRANSFORMATION." International Journal of Modern Physics B 25, no. 18 (2011): 2449–60. http://dx.doi.org/10.1142/s0217979211101387.

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A Lie algebra which consists of linear combinations of one basis of the Lie algebra A1 is presented for which an isospectral Lax pair is exhibited. By using the zero curvature equation, the generalized mKdV equation, Liouville equation and sine-Gordon equation, sinh-Gordon equation are generated via polynomial expansions. Finally, we investigate a kind of formal Bäcklund transformation for the generalized sine-Gordon equation. The explicit Bäcklund transformation of the standard sine-Gordon equation is presented. The other equations given in the paper are obtained similarly.

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33

Chen, Hsuan-Yu, and Chiachung Chen. "Comparison of Classical and Inverse Calibration Equations in Chemical Analysis." Sensors 24, no. 21 (2024): 7038. http://dx.doi.org/10.3390/s24217038.

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Chemical analysis adopts a calibration curve to establish the relationship between the measuring technique’s response and the target analyte’s standard concentration. The calibration equation is established using regression analysis to verify the response of a chemical instrument to the known properties of materials that served as standard values. An adequate calibration equation ensures the performance of these instruments. There are two kinds of calibration equations: classical equations and inverse equations. For the classical equation, the standard values are independent, and the instrumen

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34

Vitanov, Nikolay K., and Zlatinka I. Dimitrova. "Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation." Journal of Theoretical and Applied Mechanics 48, no. 1 (2018): 59–68. http://dx.doi.org/10.2478/jtam-2018-0005.

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AbstractWe consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

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35

Shaaban, Abdallah. "The Pressure Problem of The Incompressible Flow Equations." International Journal of Aeronautical Science & Aerospace Research 1, no. 1e (2014): 1–2. https://doi.org/10.19070/2470-4415-140001e.

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Numerical solutions for the incompressible flow equations encounter a numerical problem because of the lack of an equation for the pressure. To resolve this problem, the continuity equation is modified or replaced to derive pressure equations. These equations are derived from: (1) analogy with the compressible flow equations by introducing a time dependent pressure term into the continuity equation, and (2) divergence of the momentum equation and the enforcement of the continuity equation. These techniques are known as the artificial compressibility (AC)

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36

Rajabova, Lutfya Nusratovna, and Farvariddin Mufazalovich Ahmadov. "Solution of a Cauchy type problem for an integral equation of Volterra type with singular kernels, when the roots of the characteristic equations are complex conjugate." BULLETIN OF THE L.N. GUMILYOV EURASIAN NATIONAL UNIVERSITY. Mathematics. Computer science. Mechanics series 146, no. 1 (2024): 25–32. http://dx.doi.org/10.32523/bulmathenu.2024/1.3.

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In this paper, we study a two-dimensional Volterra type integral equation with a singularity and a logarithmic singularity for one variable and a strong singularity for another variable. The solution of an integral equation with special kernels in the case when the coefficients of the equation are interconnected is reduced to solving one-dimensional Volterra-type integral equations with special kernels. Using the connection of the considered integral equations with ordinary differential equations with singular coefficients, depending on the sign of the coefficients of the equation, explicit so

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37

Tarasenko, Anna, Oleksandr Karelin, Manuel Gonzalez-Hernandez, and Joselito Medina-Marin. "On the Iterated Method for the Solution of Functional Equations with Shift Whose Fixed Points are Located at the Ends of a Contour." WSEAS TRANSACTIONS ON MATHEMATICS 23 (December 15, 2024): 874–79. https://doi.org/10.37394/23206.2024.23.90.

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In this paper, we offer an approach for solving functional equations containing a shift operator and its iterations. With the help of an algorithm, the initial equation is reduced to the first iterated equation, then, applying the same algorithm, we obtain the second iterated equation. Continuing this process, we obtain the n-th iterated equation and the limit iterated equation. We prove a theorem on the equivalence of the initial equation and the iterated equations. Based on the analysis of the solvability of the limit equation, we find a solution to the initial equation. Equations of this ty

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38

ZADOROZHNAYA, Olga V., and Vladimir K. KOCHETKOV. "INTEGRAL REPRESENTATION OF SOLUTIONS OF AN ORDINARY DIFFERENTIAL EQUATION AND THE LOEWNER– KUFAREV EQUATION." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 67 (2020): 28–39. http://dx.doi.org/10.17223/19988621/67/3.

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The article presents a method of integral representation of solutions of ordinary differential equations and partial differential equations with a polynomial right-hand side part, which is an alternative to the construction of solutions of differential equations in the form of different series. The method is based on the introduction of additional analytical functions establishing the equation of connection between the introduced functions and the constituent components of the original differential equation. The implementation of the coupling equations contributes to the representation of solu

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39

Wang, Haifeng, and Chuanzhong Li. "Bäcklund transformation of Frobenius Painlevé equations." Modern Physics Letters B 32, no. 17 (2018): 1850181. http://dx.doi.org/10.1142/s0217984918501816.

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In this paper, in order to generalize the Painlevé equations, we give a [Formula: see text]-Painlevé IV equation which can apply Bäcklund transformations to explore. And these Bäcklund transformations can generate new solutions from seed solutions. Similarly, we also introduce a Frobenius Painlevé I equation and Frobenius Painlevé III equation. Then, we find the connection between the Frobenius KP hierarchy and Frobenius Painlevé I equation by the Virasoro constraint. Further, in order to seek different aspects of Painlevé equations, we introduce the Lax pair, Hirota bilinear equation and [For

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Iskandarova, Gulistan, and Dogan Kaya. "Symmetry solution on fractional equation." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 7, no. 3 (2017): 255–59. http://dx.doi.org/10.11121/ijocta.01.2017.00498.

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As we know nearly all physical, chemical, and biological processes in nature can be described or modeled by dint of a differential equation or a system of differential equations, an integral equation or an integro-differential equation. The differential equations can be ordinary or partial, linear or nonlinear. So, we concentrate our attention in problem that can be presented in terms of a differential equation with fractional derivative. Our research in this work is to use symmetry transformation method and its analysis to search exact solutions to nonlinear fractional partial differential eq

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De la Sen, M. "Asymptotic Comparison of the Solutions of Linear Time-Delay Systems with Point and Distributed Lags with Those of Their Limiting Equations." Abstract and Applied Analysis 2009 (2009): 1–37. http://dx.doi.org/10.1155/2009/216746.

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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. Both differential equations involve point and distributed delayed dynamics including Volterra class dynamics. The proofs are based on a Perron-type theorem for functional equations so that the comparison is governed by the real part of a dominant zero of the characteristic equation of the nominal

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Zhang, Shu Hua, Xiao Jing Yuan, and Qian Yin. "Discontinuous Galerkin (DG) Finite Element Method for the Improved Stokes Equations." Advanced Materials Research 250-253 (May 2011): 291–97. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.291.

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In this paper, firstly, discontinuous Galerkin method for improved Stokes equation is proposed. We derive a discontinuous Galerkin (DG) finite element formulation for the improved Stokes equations. Special case of the generalized solution equation for linear and stationary improved Stokes equations retrogresses into generalized solution equation for classical Stokes equation. It is proved that the classical solution and the generalized solution is consistent for the improved Stokes equations, existence and uniqueness of generalized solution for the improved Stokes equations are also proved.

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Kumar, Nand Kishor. "Relationship Between Differential Equations and Difference Equation." NUTA Journal 8, no. 1-2 (2021): 88–93. http://dx.doi.org/10.3126/nutaj.v8i1-2.44113.

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The study of Differential equations and Difference equations play animportant and significant role in many sciences. These equations are used as mathematical tool used in solving various problems in modeling,physics, chemistry,biology, anthropology, etc. or even in social studies. Differential equations are used to solve real life problems by approximation of numerical methods. Theory of Differential and Difference equations has been taught at all levels in high schools and at the universities for all students, including students majoring in Mathematics. This is a micro –study in which t

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Bruening, James, and Hao Hao Wang. "An Implicit Equation Given Certain Parametric Equations." Missouri Journal of Mathematical Sciences 18, no. 3 (2006): 213–20. http://dx.doi.org/10.35834/2006/1803213.

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daiah, P. Red. "Deriving Equations for Energy Equation by Fem." International Journal of Mathematics Trends and Technology 50, no. 2 (2017): 121–24. http://dx.doi.org/10.14445/22315373/ijmtt-v50p518.

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Zun-Tao, Fu, Liu Shi-Da, and Liu Shi-Kuo. "Solving Nonlinear Wave Equations by Elliptic Equation." Communications in Theoretical Physics 39, no. 5 (2003): 531–36. http://dx.doi.org/10.1088/0253-6102/39/5/531.

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Wilczyński, Paweł. "Planar nonautonomous polynomial equations: The Riccati equation." Journal of Differential Equations 244, no. 6 (2008): 1304–28. http://dx.doi.org/10.1016/j.jde.2007.12.008.

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Mach, Andrzej. "On Some Functional Equations Involving Babbage Equation." Results in Mathematics 51, no. 1-2 (2007): 97–106. http://dx.doi.org/10.1007/s00025-007-0261-5.

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Hongler, M. O., and L. Streit. "Generalized master equations and the telegrapher's equation." Physica A: Statistical Mechanics and its Applications 165, no. 2 (1990): 196–206. http://dx.doi.org/10.1016/0378-4371(90)90191-t.

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Ostaszewski, A. J. "Homomorphisms from functional equations: the Goldie equation." Aequationes mathematicae 90, no. 2 (2015): 427–48. http://dx.doi.org/10.1007/s00010-015-0357-z.

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