Solving nonlinear fractional differential equations via quadratic interpolation and Picard’s iteration

In this paper, we present a novel and efficient numerical method for solving a broad class of nonlinear fractional differential equations. Our approach uses interpolation techniques in conjunction with Picard’s iterations to solve an equivalent nonlinear Volterra integral equation. We prove a convergence theorem and validate our theoretical results through several numerical examples that demonstrate the method’s accuracy. A key advantage of this method is that it does not require solving nonlinear or linear systems during its implementation, and the sufficient condition for convergence is solely the Lipschitz continuity of the function involved in the equation.