Stability analysis of initial value problem of pantograph-type implicit fractional differential equations with impulsive conditions

Abstract

Abstract In this paper, we study an initial value problem for a class of impulsive implicit-type fractional differential equations (FDEs) with proportional delay terms. Schaefer’s fixed point theorem and Banach’s contraction principle are the key tools in obtaining the required results. We apply our results to a numerical problem for demonstration purpose.

Keywords

• Pantograph differential equations
• Initial value problem
• Impulsive condition
• Hyers–Ulam stability