SOLVABILITY OF QUADRATIC HADAMARD-TYPE FRACTIONAL INTEGRAL EQUATIONS IN ORLICZ SPACES
Mohamed M. A. Metwali
Abstract
We demonstrate some properties of Hadamard fractional operators such as boundedness, monotonicity, continuity, and acting conditions in Orlicz spaces Lφ. We apply these properties with a proper measure of noncompactness (MNC) to inspect the existence of monotonic solutions of some general, but abstract, form of quadratic Hadamard-type fractional integral equations in Lφ. We also discuss the uniqueness of the solution.
Topics & Concepts
MathematicsHadamard transformUniquenessMonotonic functionType (biology)Quadratic equationHadamard three-lines theoremPure mathematicsMathematical analysisMeasure (data warehouse)Hadamard productGeometryBiologyDatabaseEcologyComputer scienceNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsAdvanced Harmonic Analysis Research