Existence and Uniqueness Results of Fractional Differential Inclusions and Equations in Sobolev Fractional Spaces

Abstract

In this work, by using the iterative method, we discuss the existence and uniqueness of solutions for multiterm fractional boundary value problems. Next, we examine some existence and uniqueness returns for semilinear fractional differential inclusions and equations for multiterm problems by using some notions and properties on set-valued maps and give some examples to explain our main results. We explore and use in this paper the fundamental properties of set-valued maps, which are needed for the study of differential inclusions. It began only in the mid-1900s, when mathematicians realized that their uses go far beyond a mere generalization of single-valued maps.

Keywords

• semilinear fractional differential inclusion
• boundary value problem
• fixed-point theorem
• set-valued maps
• iterative methods
• Riemann–Liouville operator