Existence And Uniqueness Of Solution For A Mixed-Type Fractional Differential Equation And Ulam-Hyers Stability

In this paper, we have discussed a special type of nonlinear boundary value problems (BVPs) which involves both the right-sided Caputo-Katugampola (CK) and the left-sided Katugampola fractional derivatives (FDs). Based on some new techniques and some properties of the Mittag-Leflier functions, we have introduced a formula of the solution for the aforementioned problem. To study the existence and uniqueness results of the solution for this problem, we have applied some known fixed point theorems (i.e., Banach's contraction principle, Schauder's fixed point theorem, nonlinear alternative of Leray-Schauder type and Schaefer's fixed point theorem). We have also studied the Ulam-Hyers stability of this problem. To illustrate the theoretical results in this work, we have given two examples.