Some inequalities on multi-functions for applying in the fractional Caputo–Hadamard jerk inclusion system

Abstract

Abstract Results reported in this paper establish the existence of solutions for a class of generalized fractional inclusions based on the Caputo–Hadamard jerk system. Under some inequalities between multi-functions and with the help of special contractions and admissible maps, we investigate the existence criteria. Fixed points and end points are key roles in this manuscript, and the approximate property for end points helps us to derive the desired result for existence theory. An example is prepared to demonstrate the consistency and correctness of analytical findings.

Keywords

• ϕ-ψ-contraction
• Caputo–Hadamard derivative
• End point
• Fixed point
• Jerk equation
• Multi-function