TY - JOUR

T1 - On linear fractional differential equations with variable coefficients

AU - Fernandez, Arran

AU - Restrepo, Joel E.

AU - Suragan, Durvudkhan

N1 - Funding Information:
The second and third authors were supported by the Nazarbayev University Program 091019CRP2120. J.E. Restrepo was also supported by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations and the Methusalem programme of the Ghent University Special Research Fund (BOF) (Grant number 01M01021). This research was funded by the Science Committee of the Ministry of Education and Science of Kazakhstan (Grant No. AP09058317 ).
Publisher Copyright:
© 2022

PY - 2022/11/1

Y1 - 2022/11/1

N2 - 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.

AB - 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.

KW - Caputo fractional derivative

KW - Fixed point theory

KW - Fractional differential equations

KW - Mittag–Leffler functions

KW - Riemann–Liouville fractional calculus

KW - Series solutions

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U2 - 10.1016/j.amc.2022.127370

DO - 10.1016/j.amc.2022.127370

M3 - Article

AN - SCOPUS:85133880055

SN - 0096-3003

VL - 432

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 127370

ER -