New concepts and results in stability of fractional differential equations

In this paper, some new concepts in stability of fractional differential equations are offered from different perspectives. Hyers–Ulam–Rassias stability as well as Hyers–Ulam stability of a certain fractional differential equation are presented. The techniques rely on a fixed point theorem in a generalized complete metric space. Some applications of our results are also provided.

► New concepts in stability of fractional differential equations are offered.
► A fixed theorem in a generalized complete metric space is used.
► Hyers–Ulam–Rassias stability as well as Hyers–Ulam stability are derived.