Results 131 to 140 of about 726 (173)

Interval Abel integral equation

Soft Computing, 2016
The authors study the solvability of the interval Abel integral equation of the form: \[ \frac{1}{\Gamma(\alpha)} \int\limits_a^t (t-s)^{\alpha-1} X(s) \text{d}s = Y(t) ,\, t \in [a, b] \tag{1} \] where \(\alpha \in (0, 1)\), \(K\) is the set of any nonempty compact intervals of the real line \(\mathbb{R}\), \(Y(\cdot) : [a, b] \to K\) being a given ...
Lupulescu, Vasile, Van Hoa, Ngo
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Abel Integral Equations

1990
Even though they have a rather specialized structure, Abel equations form an important class of integral equations in applications. This happens because completely independent problems lead to the solution of such equations. After an initial survey of Abel integral equations, this chapter focuses on the numerical solution of these equations when the ...
R. S. Anderssen, F. R. Hoog
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Numerical solution of the abel integral equation

BIT, 1973
A numerical method for the solution of the Abel integral equation is presented. The known function is approximated by a sum of Chebyshev polynomials. The solution can then be expressed as a sum of generalized hypergeometric functions, which can easily be evaluated, using a simple recurrence relation.
Piessens, R., Verbaeten, P.
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Abel’s Integral Equation

1995
The following Volterra integral equation of the first kind is due to Abel (1823): $$g(x) = \int\limits_a^x {\frac{{f(y)}} {{\sqrt {x - y} }}dy\;for\;x \geqslant a}$$ (6.1.1) . Since the denominator \(\sqrt {x - y} \) has a zero at y=x, the integral in (1) is to be understood in the improper sense (cf.
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A nonlinear Abel integral equation

2006
For the general nonlinear Abel integral equation $$\frac{1}{{\Gamma (\alpha )}}\int\limits_0^x {(x - t)^{\alpha - 1} K(x,t,u(t))dt = f(x),{\text{ 0}} \leqslant x \leqslant 1,0 < \alpha < 1,}$$ some theorems on existence and uniqueness of solutions in L P , 1≤p≤∞, and in C[0, 1] are established.
Dang Dinh Ang, Rudolf Gorenflo
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Abel’s and Related Integral Equations

2000
In this chapter we give the solutions of Abel’s and some related integral equations. In the first section we present two methods for the solution of Abel’s equation and by using similar techniques solve some integral equations that can be reduced to Abel’s equation in the next section.
Ricardo Estrada, Ram P. Kanwal
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An Existence Theorem for Abel Integral Equations

SIAM Journal on Mathematical Analysis, 1974
An existence and smoothness theorem is given for the Abel integral equation $\int _0^s K(s,t)f(t)(s^p - t^p )^{ - \alpha } dt = g(s)$, $0 0$ and $0 < \alpha < 1$. Particular attention is given to the behavior of $g(s)$ and $f(s)$ about $s = 0$.
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Abel’s Integral Equation and Singular Integral Equations

2011
Abel’s integral equation occurs in many branches of scientific fields [1], such as microscopy, seismology, radio astronomy, electron emission, atomic scattering, radar ranging, plasma diagnostics, X-ray radiography, and optical fiber evaluation. Abel’s integral equation is the earliest example of an integral equation [2].
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Numerical Schemes for the Generalized Abel’s Integral Equations

International Journal of Applied and Computational Mathematics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kumar, Kamlesh, Pandey, Rajesh K., Sharma, Shiva   +2 more
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A new operational method to solve Abel’s and generalized Abel’s integral equations

Applied Mathematics and Computation, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
K. Sadri, A. Amini, C. Cheng
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