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

DOI10.1515/fca-2019-0040zbMath1428.34009OpenAlexW2791114079MaRDI QIDQ2328633

Loïc Bourdin

Publication date: 10 October 2019

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/fca-2019-0040

zbMATH Keywords

Cauchy problemfractional calculusCaputo derivativeRiemann-Liouville derivativeBielecki normRiemann-Liouville integralweighted integrabilityweighted Hölder continuityCarathéodory dynamicsexistence/uniqueness of a solution

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear ordinary differential equations and systems (34A34) Fractional derivatives and integrals (26A33) Fractional ordinary differential equations (34A08)

Related Items (5)

Optimal feedback in a linear-quadratic optimal control problem for a fractional-order system ⋮ On the relationship between the Pontryagin maximum principle and the Hamilton-Jacobi-Bellman equation in optimal control problems for fractional-order systems ⋮ Sign of the solutions of linear fractional differential equations and some applications ⋮ Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints ⋮ On representation formulas for solutions of linear differential equations with Caputo fractional derivatives

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Functional analysis, Sobolev spaces and partial differential equations
• Modification of the application of a contraction mapping method on a class of fractional differential equation.
• Nonlinear differential equations of fractional order in the space of integrable functions.
• Cauchy-Lipschitz theory for fractional multi-order dynamics: state-transition matrices, Duhamel formulas and duality theorems.
• Existence of a weak solution for fractional Euler-Lagrange equations
• On the existence and uniqueness and formula for the solution of R-L fractional cauchy problem in ℝ n
• An extension of picard-lindelöff theorem to fractional differential equations^*
• Differential Equations of Fractional Order: Methods, Results and Problems. II
• Some existence theorems on differential equations of generalized order.

This page was built for publication: Weighted Hölder continuity of Riemann-Liouville fractional integrals -- application to regularity of solutions to fractional Cauchy problems with Carathéodory dynamics