Results 111 to 120 of about 510 (151)
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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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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
2006For 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
2000In 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, 1974An 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
2011Abel’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, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kumar, Kamlesh +2 more
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A new operational method to solve Abel’s and generalized Abel’s integral equations
Applied Mathematics and Computation, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
K. Sadri, A. Amini, C. Cheng
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Systems of Generalized Abel Integral Equations.
1977Abstract : A method is presented for solving systems of generalized Abel integral equations by reduction to equivalent coupled Riemann-Hilbert boundary value problems. It is demonstrated how the Riemann system may be uncoupled and closed form solutions computed.
J. R. Walton, M. Lowengrub
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Regularization of the Abel Integral Equation with Perturbation
Computational Mathematics and Mathematical Physics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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