Multipoint boundary value problems for higher-order Hadamard fractional neutral differential equations and inclusions

Abstract

Abstract In this paper, we consider fractional neutral differential equations with multipoint boundary value conditions involving Hadamard derivatives and integrals. We obtain the existence and uniqueness of the solution of the equation by using several fixed point theorems, and we also consider the Ulam–Hyers stability of the solution. In addition, we study the differential inclusion problem with multipoint boundary value conditions and prove the existence of the solution of the boundary value problem when the multivalued map has convex values. We also give several examples to illustrate the feasibility of the results.

Keywords

• Hadamard fractional derivative
• Fractional differential inclusion
• Existence
• Boundary value problem
• Fixed point