A New Approach for the Solution of the Generalized Abel Integral Equation

The famous tautochrone problem is solved firstly by Abel in 1820s. Although the fractional calculus is known with the name of Caputo since his valuable contributions to the theory, the findings of Abel through the solutions of this famous problem may be the first realization of the differentiation and integration of fractional order. Maybe the most well-known fractional type integral equation, the generalized Abel integral equation, was solved by Abel. In this study, an approximate solution of the generalized Abel integral equation is obtained via the generalized binomial theorem.