About Solution of the Nonlinear Generalized Abel Integral Equation
DOI:
https://doi.org/10.24203/ajfam.v7i1.5620Keywords:
integral equation, Abel integral equation, tautochron problem, improper integral, Euler integral, computer mathematics system Maple.Abstract
As is known, many problems of electronics, nuclear physics, optics and astrophysics, etc. are described by the Abel integral equation of the first kind. In this paper we consider the nonlinear generalized Abel equation and show that its solution can be represented as an integral of a power function. It is shown that the constructed analytical solution and the symbolic solution obtained by means of the computer mathematics system Maple coincides, and their planar and spatial graphs are presented.
References
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R. Gorenflo, R. and S. Vessella, S. (1991) Abel integral equations, Lecture Notes in Mathematics, 1461, Springer, Berlin.
Kosarev, E. (1980) Applications of integral equations of the first kind in experiment physics, Comput. Phys. Commun. 20, 69–75.
Muintz, G. (1934) Integral Equations. Part one. Linear Volterra equations, Moscow, GTTI.
]6] Plato, R. (2005) Fractional multistep methods for weakly singular Volterra integral equations of the first kind with perturbed data, Numer. Funct. Anal. Optim. 26, 249–269.
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