Weighted Hölder continuity of Riemann-Liouville fractional integrals - Application to regularity of solutions to fractional Cauchy problems with Carathéodory dynamics

Loïc Bourdin (1)

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information

This paper is dedicated to several original (weighted) Hölder continuity results for Riemann-Liouville fractional integrals of weighted integrable functions. As an application, we prove a new weighted continuity result for solutions to nonlinear Riemann-Liouville fractional Cauchy problems with Carathéodory dynamics.

Mots clés: Riemann-Liouville integral; Riemann-Liouville derivative; Caputo derivative; Cauchy problem; Carathéodory dynamic; existence/uniqueness of a solution; weighted integrability; weighted Hölder continuity; Bielecki norm; Fractional calculus

Domaines: Systèmes dynamiques [math.DS]; Mathématiques [math]

Loïc Bourdin. Weighted Hölder continuity of Riemann-Liouville fractional integrals - Application to regularity of solutions to fractional Cauchy problems with Carathéodory dynamics. Fractional Calculus and Applied Analysis, 2019, 22 (3), pp.722-749. ⟨hal-01726069⟩