Approximate controllability of Sobolev-type Atangana-Baleanu fractional differential inclusions with noise effect and Poisson jumps
A. M. Sayed Ahmed, Hamdy M. Ahmed, Nesreen Sirelkhtam Elmki Abdalla, Assmaa Abd‐Elmonem, E. M. Mohamed
Abstract
<abstract><p>In this paper, we explore the approximative controllability of fractional stochastic differential inclusions (SDIs) of Sobolev-type with fractional derivatives in Atangana-Baleanu (AB) sense and Poisson jumps. Our findings are supported by the fixed point theorem, multi-valued map theory, compact semigroup theory and stochastic analysis principles. In the later part, an illustration is provided to clarify the established outcomes.</p></abstract>
Topics & Concepts
MathematicsControllabilitySobolev spaceDifferential inclusionFixed-point theoremType (biology)SemigroupPoisson distributionPure mathematicsMathematical analysisApplied mathematicsStatisticsBiologyEcologyNonlinear Differential Equations AnalysisStability and Controllability of Differential EquationsFractional Differential Equations Solutions