Nonlocal integro-multistrip-multipoint boundary value problems for $ \overline{\psi}_{*} $-Hilfer proportional fractional differential equations and inclusions

Abstract

In the present paper, we establish the existence criteria for solutions of single valued and multivalued boundary value problems involving a $ \overline{\psi}_{*} $-Hilfer fractional proportional derivative operator, subject to nonlocal integro-multistrip-multipoint boundary conditions. We apply the fixed-point approach to obtain the desired results for the given problems. The obtained results are well-illustrated by numerical examples. It is important to mention that several new results appear as special cases of the results derived in this paper (for details, see the last section).

Keywords

• fractional differential equations
• fractional differential inclusions
• $ \overline{\psi}_{*} $-hilfer fractional derivative
• proportional fractional derivative
• nonlocal boundary conditions
• existence
• fixed point