Analytical Approximate Solutions for Differential Equations with Generalized Caputo-type Fractional Derivatives

This study provides analytical approximate solutions to classes of nonlinear differential equations with generalized Caputo-type fractional derivatives. The Adomian decomposition method is successfully extended and modified to handle the considered fractional models. Our study displays the useful features of the modified scheme as an effective technique for providing series solutions to differential equations involving the studied fractional derivatives. Analytical solutions to generalized Caputo-type fractional derivative models are discussed and numerical comparisons with a predictor-corrector method are made to verify the applicability, accuracy and efficiency of the method. The influence of the generalized fractional derivative parameters on the dynamics of the studied fractional models is discussed. The used modified method is expected to be effectively employed to handle numerous generalized Caputo-type fractional derivative models. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.