Fractional integration by parts and Sobolev-type inequalities for ψ-fractional operators

Torres Ledesma C.E.; Sousa J.V.D.C. · Mathematical Methods in the Applied Sciences (2022) · DOI: 10.1002/mma.8348

Resumen

In the present paper, we investigate the Hardy–Littlewood type and the integration by parts result for (Formula presented.) –Riemann–Liouville fractional integrals. Also, we attack the integration by parts for the (Formula presented.) –Riemann–Liouville and (Formula presented.) –Hilfer fractional derivatives. To finish, we investigated Sobolev-type inequalities involving the (Formula presented.) –Riemann–Liouville and the (Formula presented.) –Hilfer fractional derivatives in weighted space.

Instituciones: Universidad Nacional de Trujillo