Summary: We obtain the approximate solution of Abel’s integral equation by using the following powerful, efficient but simple methods:
(i) He’s homotopy perturbation method (HPM),
(ii) Modified homotopy perturbation method (MHPM),
(iii) Adomian decomposition method (ADM) and
(iv) Modified Adomian decomposition method (MADM). The validity and applicability of these techniques are illustrated through various particular cases which demonstrate their efficiency and simplicity in solving these types of integral equations compared with the other existing methods.