Abel’s and Related Integral Equations

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. The range of the parameter α appearing in Abel’s equation is extended in the third section, while in the fourth, we generalize our analysis to equations over a simple contour in the complex plane. Equations involving combinations of both the Abel integral operator and its adjoint over open and closed contour are considered in Sections 2.5 and 2.6. Several examples are solved in the last section.