Qualitative analysis of nonlinear implicit neutral differential equation of fractional order

Abstract

In this paper, we discuss sufficient conditions for the existence of solutions for a class of Initial value problem for an neutral differential equation involving Caputo fractional derivatives. Also, we discuss some types of Ulam stability for this class of implicit fractional-order differential equation. Some applications and particular cases are presented. Finally, the existence of at least one mild solution for this class of implicit fractional-order differential equation on an infinite interval by applying Schauder fixed point theorem and the local attractivity of solutions are proved.

Keywords

• neutral differential equation
• caputo fractional derivative
• ulam stability
• ulam-hyers stability
• mild solution
• attractivity of solutions