Abel Integral Equations

Sudeshna Banerjea and Birendra Nath Mandal
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Sudeshna Banerjea: Jadavpur University, Department of Mathematics
Birendra Nath Mandal: Indian Statistical Institute, Physics and Applied Mathematics Unit

Chapter Chapter 5 in Integral Equations and Integral Transforms, 2023, pp 97-106 from Springer

Abstract: Abstract The simplest form of the Abel integral equation is given by $$\int _{0}^{x}\frac{\phi (t)}{(x-t)^{\frac{1}{2}}}dt=f(x),~~x>0,~f(0)=0$$ which is a Volterra integral equation of the first kind. Here, we shall solve the Abel integral equation using a very simple method based on elementary integration.

Date: 2023
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DOI: 10.1007/978-981-99-6360-7_5

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