A survey on random fractional differential equations involving the
generalized Caputo fractional-order derivative
Abstract
The main content of this paper is focusing on introducing a general form
of random fractional differential equations (RFDEs) with the concept of
a Caputo-type fractional derivative with respect to another function.
The problem proposed here allows us to interpolate various types of
RFDEs. By applying the fixed point theorem, the results of the existence
and uniqueness of a solution of RFDE are presented. Furthermore, we also
propose a new technique called the Hybrid Laplace-like transform method
(HLTM) to solve the solutions of RFDEs in the nonlinear form. To
visualize the theoretical results, some examples and numerical
simulations are provided.