An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space

Abstract Our aim in this paper is presenting an attractive numerical approach giving accurate solution to the nonlinear fractional Abel differential equation based on a reproducing kernel algorithm with model endowed Caputo–Fabrizio derivative. By means of such approach, we utilize Gram–Schmidt orthogonalization process create orthonormal set bases that leads appropriate Hilbert space $\mathcal{H}^{2}[a,b]$ H 2 [ a , b ] . We investigate and discuss stability convergence proposed method. The n -term series converges uniformly analytic solution. present several examples potential interests illustrate reliability, efficacy, performance method under influence gained results have shown superiority its infinite accuracy least time efforts solving Abel-type model. Therefore, direction, alternative systematic tool for analyzing behavior many temporal equations emerging fields engineering, physics, sciences.