Fuzzy fractional differential equations under Caputo-Katugampola fractional derivative approach

In this work, an initial value problem of Caputo–Katugampola (CK) fractional differential equations in fuzzy setting is considered and an idea of successive approximations under generalized Lipschitz condition is used to prove the existence and uniqueness results of the solution to the given problem. In order to obtain the above results, some necessary comparison theorems in real-valued differential equation under CK fractional derivative are established. Finally, a new technique to find analytical solutions of CK fuzzy fractional differential equations by using the solutions of fuzzy integer order differential equations is proposed. Some examples illustrating the applications of our results are presented.