On the existence and Ulam-Hyers stability for implicit fractional differential equation via fractional integral-type boundary conditions

Abstract

This study investigates the existence of solutions for implicit fractional differential equations with fractional-order integral boundary conditions. We create the required conditions to ensure unique solution and Ulam-Hyers-Rassias stability. We also give examples to highlight the major findings.

Keywords

• implicit fractional-order differential equation
• existence results
• green’s function
• boundary value problems
• ulam-hyers stability
• 26a33
• 34k45
• 47g10