Fractional integration by parts and Sobolev‐type inequalities for ψ$$ \psi $$‐fractional operators
César E. Torres Ledesma, José Vanterler da C. Sousa
Abstract
In the present paper, we investigate the Hardy–Littlewood type and the integration by parts result for –Riemann–Liouville fractional integrals. Also, we attack the integration by parts for the –Riemann–Liouville and –Hilfer fractional derivatives. To finish, we investigated Sobolev‐type inequalities involving the –Riemann–Liouville and the –Hilfer fractional derivatives in weighted space.
Topics & Concepts
MathematicsType (biology)Sobolev spaceFractional calculusPure mathematicsRiemann hypothesisSpace (punctuation)Sobolev inequalityMathematical analysisInequalityBiologyEcologyLinguisticsPhilosophyAdvanced Harmonic Analysis ResearchDifferential Equations and Boundary ProblemsNonlinear Differential Equations Analysis