Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 04/2017, Volume 471, pp. 212 - 218

A one-parameter family of Emden–Fowler equations defined by Lampariello’s parameter p which, upon using Thomas–Fermi boundary conditions, turns into a set of...

Abel equation | Invariant | Generalized Thomas–Fermi equation | Emden–Fowler equation | Dynamical systems | Emden-Fowler equation | PHYSICS, MULTIDISCIPLINARY | Generalized Thomas Fermi equation | Mathematics - Dynamical Systems

Abel equation | Invariant | Generalized Thomas–Fermi equation | Emden–Fowler equation | Dynamical systems | Emden-Fowler equation | PHYSICS, MULTIDISCIPLINARY | Generalized Thomas Fermi equation | Mathematics - Dynamical Systems

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 04/2016, Volume 39, Issue 6, pp. 1376 - 1387

We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied...

Appel invariant | canonical form | Abel equation | third‐order hyperbolic function | normal form | third-order hyperbolic function | MATHEMATICS, APPLIED | Nonlinearity | Hyperbolic functions | Integral calculus | Integral equations | Mathematical analysis | Oscillators

Appel invariant | canonical form | Abel equation | third‐order hyperbolic function | normal form | third-order hyperbolic function | MATHEMATICS, APPLIED | Nonlinearity | Hyperbolic functions | Integral calculus | Integral equations | Mathematical analysis | Oscillators

Journal Article

Soft Computing, ISSN 1432-7643, 05/2017, Volume 21, Issue 10, pp. 2777 - 2784

In this paper, we use a generalization of the Riemann-Liouville fractional integral for interval-valued functions to study a theory of the interval Abel...

Interval Abel integral equation | Interval-valued Riemann–Liouville fractional integral | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HUKUHARA DIFFERENTIABILITY | CALCULUS | DIFFERENTIAL-EQUATIONS | Interval-valued Riemann-Liouville fractional integral | VALUED FUNCTIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Interval Abel integral equation | Interval-valued Riemann–Liouville fractional integral | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HUKUHARA DIFFERENTIABILITY | CALCULUS | DIFFERENTIAL-EQUATIONS | Interval-valued Riemann-Liouville fractional integral | VALUED FUNCTIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 07/2019, Volume 525, pp. 1203 - 1211

In this article, with the aid of the entire Riemann functional equation (ERFE), defined by ξs=12ss−1π−s2Γs2ςs, where s is a complex variable, Γs is the Euler’s...

Euler–Maclaurin–Siegel summation formula | Entire Riemann functional equation | Riemann Zeta function | Critical line | Riemann hypothesis | Abel–Plana summation formula | Abel-Plana summation formula | PHYSICS, MULTIDISCIPLINARY | Euler-Maclaurin-Siegel summation formula | Rock mechanics

Euler–Maclaurin–Siegel summation formula | Entire Riemann functional equation | Riemann Zeta function | Critical line | Riemann hypothesis | Abel–Plana summation formula | Abel-Plana summation formula | PHYSICS, MULTIDISCIPLINARY | Euler-Maclaurin-Siegel summation formula | Rock mechanics

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 08/2015, Volume 25, Issue 1-3, pp. 102 - 117

•A small dispersion effect is introduced to the (2+1)-dimensional KP–BBM equation.•Dynamical system theory is applied to find bounded traveling wave...

(2 + 1) dimensional KP–BBM equation | Weirstrass [formula omitted] function | Dynamical system | Jacobi elliptic function | (2+1) dimensional KP-BBM equation | Weirstrass function | MATHEMATICS, APPLIED | FACTORIZATIONS | PHYSICS, FLUIDS & PLASMAS | STRAITS | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI EQUATION | ABEL DIFFERENTIAL-EQUATION | WATER-WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Weirstrass p function | BONA-MAHONEY EQUATION | SOLITONS | SOLITARY WAVES | POWER-LAW NONLINEARITY | DEPTH | Mathematical analysis | Bifurcations | Traveling waves | Mathematical models | Transformations | Stability analysis | Dispersions | Elliptic functions

(2 + 1) dimensional KP–BBM equation | Weirstrass [formula omitted] function | Dynamical system | Jacobi elliptic function | (2+1) dimensional KP-BBM equation | Weirstrass function | MATHEMATICS, APPLIED | FACTORIZATIONS | PHYSICS, FLUIDS & PLASMAS | STRAITS | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI EQUATION | ABEL DIFFERENTIAL-EQUATION | WATER-WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Weirstrass p function | BONA-MAHONEY EQUATION | SOLITONS | SOLITARY WAVES | POWER-LAW NONLINEARITY | DEPTH | Mathematical analysis | Bifurcations | Traveling waves | Mathematical models | Transformations | Stability analysis | Dispersions | Elliptic functions

Journal Article

Physics of Fluids, ISSN 1070-6631, 04/2016, Volume 28, Issue 4, p. 46102

Hyperbolic two-phase flow models have shown excellent ability for the resolution of a wide range of applications ranging from interfacial flows to fluid...

2-PHASE FLOW | MECHANICS | TO-DETONATION TRANSITION | MULTIPHASE MIXTURES | COMPRESSIBLE FLUIDS | PHYSICS, FLUIDS & PLASMAS | LIQUID | INTERFACES | MODEL | SIMULATION | GRANULAR-MATERIALS | RIEMANN PROBLEM | Compressibility | Two phase flow | Parameters | Partial differential equations | Computational fluid dynamics | Saturation | Enthalpy | Acoustic propagation | Vapors | Boundary conditions | Internal energy | Equations of state | Wave propagation | Mathematical models | Hyperbolic systems | Thermics | Analysis of PDEs | Mechanics | Reactive fluid environment | Fluids mechanics | Mathematics | Engineering Sciences | VELOCITY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CALCULATION METHODS | RESOLUTION | WAVE PROPAGATION | FLOW RATE | COMPARATIVE EVALUATIONS | TWO-PHASE FLOW | BOUNDARY CONDITIONS | DIAGRAMS | MIXTURES | VAPORS | ENTHALPY | PARTIAL DIFFERENTIAL EQUATIONS | EQUATIONS OF STATE | FLOW MODELS | SATURATION | ENGINEERING | ENTROPY | LIQUIDS

2-PHASE FLOW | MECHANICS | TO-DETONATION TRANSITION | MULTIPHASE MIXTURES | COMPRESSIBLE FLUIDS | PHYSICS, FLUIDS & PLASMAS | LIQUID | INTERFACES | MODEL | SIMULATION | GRANULAR-MATERIALS | RIEMANN PROBLEM | Compressibility | Two phase flow | Parameters | Partial differential equations | Computational fluid dynamics | Saturation | Enthalpy | Acoustic propagation | Vapors | Boundary conditions | Internal energy | Equations of state | Wave propagation | Mathematical models | Hyperbolic systems | Thermics | Analysis of PDEs | Mechanics | Reactive fluid environment | Fluids mechanics | Mathematics | Engineering Sciences | VELOCITY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CALCULATION METHODS | RESOLUTION | WAVE PROPAGATION | FLOW RATE | COMPARATIVE EVALUATIONS | TWO-PHASE FLOW | BOUNDARY CONDITIONS | DIAGRAMS | MIXTURES | VAPORS | ENTHALPY | PARTIAL DIFFERENTIAL EQUATIONS | EQUATIONS OF STATE | FLOW MODELS | SATURATION | ENGINEERING | ENTROPY | LIQUIDS

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 8/2019, Volume 59, Issue 8, pp. 1292 - 1313

A two-point boundary value problem is considered for the Emden–Fowler equation, which is a singular nonlinear ordinary differential equation of the second...

Computational Mathematics and Numerical Analysis | Painlevé test | Emden–Fowler equation | Mathematics | Abel equation of the second kind | Fuchs index | Thomas–Fermi problem | parametric representation | Painleve test | MATHEMATICS, APPLIED | Emden-Fowler equation | Thomas-Fermi problem | ABEL | EXACT ANALYTIC SOLUTIONS | MODEL | PHYSICS, MATHEMATICAL | CHEBYSHEV SERIES | Computer science | Algorithms | Differential equations | Charged ions | Boundary value problems | Representations

Computational Mathematics and Numerical Analysis | Painlevé test | Emden–Fowler equation | Mathematics | Abel equation of the second kind | Fuchs index | Thomas–Fermi problem | parametric representation | Painleve test | MATHEMATICS, APPLIED | Emden-Fowler equation | Thomas-Fermi problem | ABEL | EXACT ANALYTIC SOLUTIONS | MODEL | PHYSICS, MATHEMATICAL | CHEBYSHEV SERIES | Computer science | Algorithms | Differential equations | Charged ions | Boundary value problems | Representations

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 2/2018, Volume 58, Issue 2, pp. 230 - 237

We consider quasi-stationary solutions of a problem without initial conditions for the Kolmogorov–Petrovskii–Piskunov (KPP) equation, which is a quasilinear...

Computational Mathematics and Numerical Analysis | Kolmogorov–Petrovskii–Piskunov equation | Abel’s equation of the second kind | Mathematics | traveling waves | intermediate asymptotic regime | self-similar solutions | generalized Fisher equation | Fuchs–Kowalewski–Painlevé test | Fuchs-Kowalewski-Painleve test | MATHEMATICS, APPLIED | EXCITATION | Abel's equation of the second kind | MODELS | CONVECTION | PHYSICS, MATHEMATICAL | Kolmogorov-Petrovskii-Piskunov equation | Computer science | Combustion | Mathematical models | Representations | Initial conditions | Construction planning | Self-similarity

Computational Mathematics and Numerical Analysis | Kolmogorov–Petrovskii–Piskunov equation | Abel’s equation of the second kind | Mathematics | traveling waves | intermediate asymptotic regime | self-similar solutions | generalized Fisher equation | Fuchs–Kowalewski–Painlevé test | Fuchs-Kowalewski-Painleve test | MATHEMATICS, APPLIED | EXCITATION | Abel's equation of the second kind | MODELS | CONVECTION | PHYSICS, MATHEMATICAL | Kolmogorov-Petrovskii-Piskunov equation | Computer science | Combustion | Mathematical models | Representations | Initial conditions | Construction planning | Self-similarity

Journal Article

Physics Letters A, ISSN 0375-9601, 09/2013, Volume 377, Issue 21-22, pp. 1434 - 1438

We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel...

Integrability | Dissipative nonlinear equations | Abel equations | SYSTEMS | PHYSICS, MULTIDISCIPLINARY | ODES | Differential equations | Nonlinear equations | Mathematical analysis | Dissipation | Solid state physics | Nonlinearity | Factorization | Joints

Integrability | Dissipative nonlinear equations | Abel equations | SYSTEMS | PHYSICS, MULTIDISCIPLINARY | ODES | Differential equations | Nonlinear equations | Mathematical analysis | Dissipation | Solid state physics | Nonlinearity | Factorization | Joints

Journal Article

Siberian Mathematical Journal, ISSN 0037-4466, 1/2019, Volume 60, Issue 1, pp. 93 - 107

We construct new radially symmetric exact solutions of the multidimensional nonlinear diffusion equation, which can be expressed in terms of elementary...

multidimensional nonlinear diffusion equation | Abel equation | nonlinear heat equation | Lambert W -function | Jacobi elliptic functions | radially symmetric exact solutions | Mathematics, general | Mathematics | self-similar solutions | Lambert W-function | MATHEMATICS

multidimensional nonlinear diffusion equation | Abel equation | nonlinear heat equation | Lambert W -function | Jacobi elliptic functions | radially symmetric exact solutions | Mathematics, general | Mathematics | self-similar solutions | Lambert W-function | MATHEMATICS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 03/2017, Volume 73, Issue 6, pp. 1346 - 1362

In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling...

Riemann–Liouville integral | Surface–volume reactions | Caputo fractional derivative | Fractional calculus | Abel integral equation | MATHEMATICS, APPLIED | SET | DIFFERENTIABILITY | GEOMETRIC INTERPRETATION | INTEGRODIFFERENTIAL CALCULUS | MODELS | DIFFUSION | Riemann-Liouville integral | DERIVATIVES | Surface-volume reactions

Riemann–Liouville integral | Surface–volume reactions | Caputo fractional derivative | Fractional calculus | Abel integral equation | MATHEMATICS, APPLIED | SET | DIFFERENTIABILITY | GEOMETRIC INTERPRETATION | INTEGRODIFFERENTIAL CALCULUS | MODELS | DIFFUSION | Riemann-Liouville integral | DERIVATIVES | Surface-volume reactions

Journal Article

1999, Mathematics in science and engineering, ISBN 0125588402, Volume 198, 366

This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the...

Numerical solutions | Fractional calculus | Differential equations | Fractions

Numerical solutions | Fractional calculus | Differential equations | Fractions

eBook

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 08/2016, Volume 302, pp. 118 - 128

The purpose of this paper is to present an approximate method for solving the Generalized Abel's integral equations. The approximate method is based on the...

Collocation method | Generalized Abel's integral equations | Approximation | Integral equations | Mathematical analysis | Collocation methods | Mathematical models | Polynomials | Volterra integral equations | Convergence

Collocation method | Generalized Abel's integral equations | Approximation | Integral equations | Mathematical analysis | Collocation methods | Mathematical models | Polynomials | Volterra integral equations | Convergence

Journal Article

14.
Full Text
A class of exact solutions of the Liénard-type ordinary nonlinear differential equation

Journal of Engineering Mathematics, ISSN 0022-0833, 12/2014, Volume 89, Issue 1, pp. 193 - 205

A class of exact solutions is obtained for the Liénard-type ordinary nonlinear differential equation. As a first step in our study, the second-order...

Abel equation | Analysis | Numeric Computing | Exact solutions | Mechanics | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | Integrability condition | Liénard equation | Physics | Differential equations | Nonlinearity | Integral calculus | Mathematical analysis

Abel equation | Analysis | Numeric Computing | Exact solutions | Mechanics | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | Integrability condition | Liénard equation | Physics | Differential equations | Nonlinearity | Integral calculus | Mathematical analysis

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2019, Volume 470, Issue 2, pp. 733 - 749

We study the number of periodic solutions of linear, Riccati and Abel dynamic equations in the time scales setting. In this way, we recover known results for...

Periodic function | Linear, Riccati and Abel differential and difference equations | Time scales | Melnikov function | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | SYSTEMS | LIMIT-CYCLES | Differential equations

Periodic function | Linear, Riccati and Abel differential and difference equations | Time scales | Melnikov function | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | SYSTEMS | LIMIT-CYCLES | Differential equations

Journal Article

Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2016, Volume 2016, Issue 64, pp. 1 - 38

New and known properties of the resolvent of the kernel of linear Abel integral equations of the form x(t) = f(t) - lambda integral(t)(0) (t - s)(q-1) x(s) ds,...

Riemann-Liouville operators | Mittag-Leffler functions | Fractional differential equations | Singular kernels | Fixed points | Resolvents | Abel integral equations | Volterra integral equations | MATHEMATICS, APPLIED | fixed points | resolvents | DIFFERENTIAL-EQUATIONS | fractional differential equations | KERNELS | MATHEMATICS | singular kernels | VOLTERRA | mittag-leffler functions | riemann–liouville operators | abel integral equations | volterra integral equations

Riemann-Liouville operators | Mittag-Leffler functions | Fractional differential equations | Singular kernels | Fixed points | Resolvents | Abel integral equations | Volterra integral equations | MATHEMATICS, APPLIED | fixed points | resolvents | DIFFERENTIAL-EQUATIONS | fractional differential equations | KERNELS | MATHEMATICS | singular kernels | VOLTERRA | mittag-leffler functions | riemann–liouville operators | abel integral equations | volterra integral equations

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2008, Volume 56, Issue 7, pp. 1748 - 1757

This paper presents a new, stable, approximate inversion of Abel integral equation. By using the Taylor expansion of the unknown function, Abel equation is...

Taylor expansion | Error analysis | Abel inversion | Approximate solution | Abel integral equation | approximate solution | MATHEMATICS, APPLIED | error analysis | Approximation | Integral equations | Mathematical analysis | Exact solutions | Inversions | Mathematical models | Derivatives

Taylor expansion | Error analysis | Abel inversion | Approximate solution | Abel integral equation | approximate solution | MATHEMATICS, APPLIED | error analysis | Approximation | Integral equations | Mathematical analysis | Exact solutions | Inversions | Mathematical models | Derivatives

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 2015, Volume 2015, Issue 1, pp. 1 - 14

Solving the boundary value problems of the heat equation in noncylindrical domains degenerating at the initial moment leads to the necessity of research of the...

Abel equation | Volterra integral equation | Carleman-Vekua regularization method | spectrum | characteristic equation | nontrivial solution | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | Functions, Abelian | Usage | Integral equations | Spectrum analysis | Analysis | Approximation theory | Methods | Kernels | Volterra equations | Mathematical analysis | Norms | Texts | Spectra | Regularization | Volterra integral equations | Heat equations

Abel equation | Volterra integral equation | Carleman-Vekua regularization method | spectrum | characteristic equation | nontrivial solution | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | Functions, Abelian | Usage | Integral equations | Spectrum analysis | Analysis | Approximation theory | Methods | Kernels | Volterra equations | Mathematical analysis | Norms | Texts | Spectra | Regularization | Volterra integral equations | Heat equations

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 01/2014, Volume 227, pp. 656 - 661

In this paper, a numerical method for solving Abel integral equation is presented. We first convert the integral equation to the algebraic equation. Then we...

Taylor expansion | Padé approximant | Laplace transform | Abel integral equation | Series solution | MATHEMATICS, APPLIED | Pade approximant | Numerical analysis | Algebra | Computation | Integral equations | Mathematical analysis | Mathematical models | Laplace transforms | Convergence

Taylor expansion | Padé approximant | Laplace transform | Abel integral equation | Series solution | MATHEMATICS, APPLIED | Pade approximant | Numerical analysis | Algebra | Computation | Integral equations | Mathematical analysis | Mathematical models | Laplace transforms | Convergence

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2017, Volume 453, Issue 1, pp. 485 - 501

Given trigonometric monomials A1,A2,A3,A4, such that A1,A3 have the same signs as sint, and A2,A4 the same signs as cost, and natural numbers n,m>1, we study...

Centers | Abel equation | Limit cycles | Periodic solutions | Smale–Pugh problem | Hilbert 16th problem | Smale-Pugh problem | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | NUMBER | DIFFERENTIAL-EQUATIONS | UNIQUENESS | MATHEMATICS | SYSTEMS

Centers | Abel equation | Limit cycles | Periodic solutions | Smale–Pugh problem | Hilbert 16th problem | Smale-Pugh problem | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | NUMBER | DIFFERENTIAL-EQUATIONS | UNIQUENESS | MATHEMATICS | SYSTEMS

Journal Article