On linear fractional differential equations with variable coefficients
作者：
Highlights：
• We study and solve linear ordinary differential equations, with fractional order derivatives of either Riemann–Liouville or Caputo types, and with variable coefficients which are either integrable or continuous functions.
• The solutions are given explicitly by a convergent infinite series involving compositions of fractional integrals, and its uniqueness is proved in suitable function spaces.
• For the case of constant coefficients, the solutions can be expressed by the multivariate Mittag–Leffler function.
摘要
•We study and solve linear ordinary differential equations, with fractional order derivatives of either Riemann–Liouville or Caputo types, and with variable coefficients which are either integrable or continuous functions.•The solutions are given explicitly by a convergent infinite series involving compositions of fractional integrals, and its uniqueness is proved in suitable function spaces.•For the case of constant coefficients, the solutions can be expressed by the multivariate Mittag–Leffler function.
论文关键词：Fractional differential equations,Riemann–Liouville fractional calculus,Caputo fractional derivative,Series solutions,Fixed point theory,Mittag–Leffler functions
论文评审过程：Received 19 February 2022, Revised 26 June 2022, Accepted 29 June 2022, Available online 9 July 2022, Version of Record 9 July 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127370
