Development on a Fractional Hybrid Differential Inclusion with a Nonlinear Nonlocal Fractional-Order Integral Inclusion

Abstract

In this article, we consider a Riemann–Liouville fractional-order nonlinear hybrid delay differential inclusion with a nonlinear set-valued nonlocal integral condition of fractional order. We prove some existence and uniqueness results in C(I,R). We also study the continuous dependence of the solutions on the two sets of selections of the two set-valued functions, considered in our problem, and on some other parameters. Finally, to validate our results, we present an example and some particular cases.

Keywords

• Riemann–Liouville derivative and integrals
• hybrid differential inclusion
• multivalued nonlocal integral condition of fractional order
• nonlinear alternative of Leray–Schauder type
• continuous dependency
• conjugate order (1−α,α)