LINEAR DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS AND MITTAG-LEFFLER KERNELS
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Date
2021-10-27
Authors
Fernandez, Arran
Restrepo, Joel E.
Suragan, Durvudkhan
Journal Title
Journal ISSN
Volume Title
Publisher
Alexandria Engineering Journal
Abstract
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 equa-
tions with variable coefficients. The corresponding results for fractional differential equations with
constant coefficients are also given
Description
Keywords
Type of access: Open Access, Fractional differential equations, Atangana–Baleanu fractional calculus, Differential equations with variable coefficients, Series solutions, Analytical solutions
Citation
Fernandez, A., Restrepo, J. E., & Suragan, D. (2022). Linear differential equations with variable coefficients and Mittag-Leffler kernels. Alexandria Engineering Journal, 61(6), 4757–4763. https://doi.org/10.1016/j.aej.2021.10.028