A new approach for solving fredholm integro-differential equations

In the present article, we extend the optimal auxiliary function method (OAFM) to integro-differential equations. The method has especially contained the auxiliary function and convergence control parameters that accelerate the method's convergence. The numerical results, obtained by the OAFM are listed with those obtained by the ADM, CAS Wavelet method, and ESA method. Further, the obtained results have been compared with the exact solution through different graphs and tables, which shows that the proposed method is very effective and easy to implement for different fractional-order PDEs.