Picard, Adomian and predictor–corrector methods for an initial value problem of arbitrary (fractional) orders differential equation

Abstract

We study the two analytical methods, the classical method of successive approximations (Picard method), Adomian decomposition method (ADM) see (Abbaoui and Cherruault, 1994; Adomian et al., 1992; Adomian, 1995) [1–3] and the (numerical method) predictor corrector method (PECE) for an initial value problem of arbitrary (fractional) orders differential equation (FDE). The existence and uniqueness of the solution will be proved and the convergence will be discussed for each method. Some examples will be studied.

Keywords

• Fractional differential equation
• Picard method
• Adomian method
• Predictor corrector method
• Convergence analysis
• Error analysis