A survey on random fractional differential equations involving the generalized Caputo fractional-order derivative

This article discusses the preliminary results of a general form of random fractional differential equations (RFDEs) involving the generalized Caputo fractional derivative. The problem proposed here allows us to interpolate various types of RFDEs. By applying the fixed point theorem and the generalized Gronwall fractional integral inequality, the existence of a unique solution and the Hyers–Ulam stability of RFDEs are presented. Furthermore, a new technique called the Hybrid Laplace-like transform method (HLTM) is proposed to seek the solutions of RFDEs in the nonlinear form. Numerical examples are provided to verify the effectiveness of the proposed method.