Abstract
In this paper, we introduce a new family of interpolants, called piecewise fractional interpolants (PFIs). The proposed interpolants are used to construct a new class of predictor–corrector methods for solving nonlinear fractional differential equations (FDEs). To construct the PFIs, it is essential to know the regularity behavior of the exact solution of an FDE. To do so, we present a pre-algorithm to provide the singular indexes of the exact solution at the initial time. Also, an error analysis with a rigorous proof of the convergence order of the proposed method is given. Some numerical examples are carried out to support the theoretical analysis.
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