Linear differential equations with variable coefficients and Mittag-Leffler kernels

Arran Fernandez, Joel E. Restrepo, Durvudkhan Suragan

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Fractional differential equations with constant coefficients can be readily handled by a number of methods, but those with variable coefficients are much more challenging. Recently, a method has appeared in the literature for solving fractional differential equations with variable coefficients, the solution being in the form of an infinite series of iterated fractional integrals. In the current work, we consider fractional differential equations with Atangana–Baleanu integro-differential operators and continuous variable coefficients, and establish analytical solutions for such equations. The representation of the solution is given by a uniformly convergent infinite series involving Atangana–Baleanu operators. To the best of our knowledge, this is the first time that explicit analytical solutions have been given for such general Atangana–Baleanu differential equations with variable coefficients. The corresponding results for fractional differential equations with constant coefficients are also given.

Original languageEnglish
Pages (from-to)4757-4763
Number of pages7
JournalAlexandria Engineering Journal
Issue number6
Publication statusAccepted/In press - 2021


  • Analytical solutions
  • Atangana–Baleanu fractional calculus
  • Differential equations with variable coefficients
  • Fractional differential equations
  • Series solutions

ASJC Scopus subject areas

  • General Engineering


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