Operational calculus for Caputo fractional calculus with respect to functions and the associated fractional differential equations

作者：

Highlights：

• Function spaces are established for Caputo fractional calculus with respect to functions.

• The formalism of Mikusinski’s operational calculus is created in this setting.

• Fractional differential equations are solved for Caputo derivatives with respect to functions.

摘要

•Function spaces are established for Caputo fractional calculus with respect to functions.•The formalism of Mikusinski’s operational calculus is created in this setting.•Fractional differential equations are solved for Caputo derivatives with respect to functions.

论文关键词：Fractional differential equations,Operational calculus,Mikusiński’s operational calculus,Fractional calculus with respect to functions,Caputo derivatives

论文评审过程：Received 23 March 2021, Revised 12 May 2021, Accepted 18 May 2021, Available online 3 June 2021, Version of Record 3 June 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126400