On linear fractional differential equations with variable coefficients

Arran Fernandez, Joel E. Restrepo and Durvudkhan Suragan

Applied Mathematics and Computation, 2022, vol. 432, issue C

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.

Keywords: Fractional differential equations; Riemann–Liouville fractional calculus; Caputo fractional derivative; Series solutions; Fixed point theory; Mittag–Leffler functions (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:432:y:2022:i:c:s0096300322004441

DOI: 10.1016/j.amc.2022.127370

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