Analysis of Hilfer Fractional Integro-Differential Equations with Almost Sectorial Operators
Kulandhaivel Karthikeyan, Amar Debbouche, Delfim F. M. Torres
Abstract
In this work, we investigate a class of nonlocal integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove our results by applying Schauder’s fixed point technique. Moreover, we show the fundamental properties of the representation of the solution by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory.
Topics & Concepts
MathematicsClass (philosophy)Applied mathematicsCompact spaceRepresentation (politics)Point (geometry)Mathematical analysisFixed-point theoremFixed pointWork (physics)Fractional calculusSet (abstract data type)Pure mathematicsType (biology)Extension (predicate logic)Nonlinear Differential Equations AnalysisFractional Differential Equations SolutionsFixed Point Theorems Analysis