Existence and Hyers–Ulam Stability of Jerk-Type Caputo and Hadamard Mixed Fractional Differential Equations

This article is concerned with existence of mild solutions for jerk-type fractional differential equations in the sense of Hadamard and Caputo fractional derivatives with separated boundary conditions. For the uniqueness of mild solutions in both cases, Banach contraction principle are followed. Moreover, at least one mild solution of jerk-type Caputo–Hadamard and Hadamard–Caputo fractional differential equations can be analyzed using Krasnoselskii’s and Leray–Schauder fixed point theorems. Hyers–Ulam stability and its generalized case for both type of mentioned jerk-type problems can be find out with the help of some conditions and definitions. For the illustration of main results, an example is provided.