On existence and stability results for nonlinear fractional delay differential equations

Abstract

We establish existence and uniqueness results for fractional order delay differential equations. It is proved that successive approximation method can also be successfully applied to study Ulam--Hyers stability, generalized Ulam--Hyers stability, Ulam--Hyers--Rassias stability, generalized Ulam--Hyers--Rassias stability, $ \mathbb{E}_{\alpha}$--Ulam--Hyers stability and generalized $ \mathbb{E}_{\alpha}$--Ulam--Hyers stability of fractional order delay differential equations.

Keywords

• Fractional delay differential equation
• Fixed point theorem
• Existence and uniqueness
• Successive approximation
• Ulam--Hyers stability
• $ \mathbb{E}_{\alpha}$--Ulam--Hyers stability.