Study of fractional order pantograph type impulsive antiperiodic boundary value problem

Abstract

Abstract In this paper, we study existence and stability results of an anti-periodic boundary value problem of nonlinear delay (pantograph) type implicit fractional differential equations with impulsive conditions. Using Schaefer’s fixed point theorem and Banach’s fixed point theorem, we have established results of at least one solution and uniqueness. Also, using the Hyers–Ulam concept, we have derived various kinds of Ulam stability results for the considered problem. Finally, we have applied our obtained results to a numerical problem.

Keywords

• Delay differential equation
• Impulsive conditions
• Schaefer’s fixed point theorem
• Hyers–Ulam stability