A reliable modification of Adomian decomposition method
Applied Mathematics and Computation
Generalized homotopy approach to multiobjective optimization
Journal of Optimization Theory and Applications
Journal of Computational and Applied Mathematics
A review of the decomposition method and some recent results for nonlinear equations
Mathematical and Computer Modelling: An International Journal
An Operational Haar Wavelet Method for Solving Fractional Volterra Integral Equations
International Journal of Applied Mathematics and Computer Science - Issues in Advanced Control and Diagnosis
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In the present paper, 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.