A Generalized NPCM for Solving Multi-Term Fractional Differential Equations

A new predictor-corrector method (NPCM) was developed by Daftardar-Gejji and Sukale et al. (Appl Math Comput 244: 158-182, 2014) to solve fractional order differential equations. In the present article, we develop a new algorithm for solving multi-term fractional differential equations. This new algorithm developed is effectively a generalization of NPCM for solving multi-term fractional differential equations and hence we refer to it as NPCM-MT. The new method NPCM-MT is a combination of implicit product trapezoidal rule and New Iterative Method (J Math Anal Appl 316(2): 753–763 2006). The NPCM-MT is compared with Fractional Adams Method (FAM) for multi-term fractional differential equations, and is found to be more time-efficient & accurate than FAM. Numerous illustrative examples are discussed here to demonstrate effectiveness of the NPCM-MT. Detailed convergence analysis of the method is given including error bounds under various types of assumptions on the equation. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.