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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
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
Journal Article
Soft Computing, ISSN 1432-7643, 05/2017, Volume 21, Issue 10, pp. 2777 - 2784
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
Journal Article
Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 8/2019, Volume 59, Issue 8, pp. 1292 - 1313
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
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
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
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
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
Journal Article
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
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
Journal Article
Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2016, Volume 2016, Issue 64, pp. 1 - 38
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
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 2015, Volume 2015, Issue 1, pp. 1 - 14
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
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 sin⁡t, and A2,A4 the same signs as cos⁡t, 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
Journal Article