On stability for nonlinear implicit fractional differential equations

Abstract

The purpose of this paper is to establish some types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of implicit fractional-order differential equation.

Keywords

• Initial value problem
• Caputo's fractional derivative
• implicit fractional differential equations
• fractional integral, existence
• Gronwall's lemma
• fixed point
• Ulam-Hyers stability
• Ulam-Hyers-Rassias stability