On linear fractional differential equations with variable coefficients

Arran Fernandez, Joel E. Restrepo, Durvudkhan Suragan

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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. In each case, the solution is given explicitly by a convergent infinite series involving compositions of fractional integrals, and its uniqueness is proved in suitable function spaces using the Banach fixed point theorem. As a special case, we consider the case of constant coefficients, whose solutions can be expressed by using the multivariate Mittag–Leffler function. Some illustrative examples with potential applications are provided.

Original languageEnglish
Article number127370
JournalApplied Mathematics and Computation
Volume432
DOIs
Publication statusPublished - Nov 1 2022

Keywords

  • Caputo fractional derivative
  • Fixed point theory
  • Fractional differential equations
  • Mittag–Leffler functions
  • Riemann–Liouville fractional calculus
  • Series solutions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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