Explicit solutions for linear variable–coefficient fractional differential equations with respect to functions

Joel E. Restrepo, Michael Ruzhansky, Durvudkhan Suragan

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite series of fractional integro-differential operators, which can be widely and efficiently used for analytic and computational purposes. In the case of constant coefficients, the solution can be expressed in terms of the multivariate Mittag-Leffler functions. In particular, the obtained result extends the Luchko-Gorenflo representation formula [1, Theorem 4.1] to a general class of linear fractional differential equations with variable coefficients, to complex fractional derivatives, and to fractional derivatives with respect to a given function.

Original languageEnglish
Article number126177
JournalApplied Mathematics and Computation
Volume403
DOIs
Publication statusPublished - Aug 15 2021

Keywords

  • Fractional calculus
  • Fractional differential equations
  • Fractional integro-differential operators
  • Mittag-Leffler functions
  • Variable coefficients

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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