On a Caputo conformable inclusion problem with mixed Riemann–Liouville conformable integro-derivative conditions

Abstract

Abstract We discuss some existence criteria for a new category of the Caputo conformable differential inclusion furnished with four-point mixed Riemann–Liouville conformable integro-derivative boundary conditions. In this way, we employ some analytical techniques on α-ψ-contractive mappings and operators having the approximate endpoint property to reach desired theoretical results. Finally, we provide an example to illustrate our last main result.

Keywords

• α-ψ-contractive mappings
• Approximate endpoint property
• Mixed integro-derivative conditions
• The Caputo conformable derivative