On linear fractional differential equations with variable coefficients

Arran Fernandez; Joel E. Restrepo; Durvudkhan Suragan

doi:10.1016/j.amc.2022.127370

On linear fractional differential equations with variable coefficients

Arran Fernandez, Joel E. Restrepo, Durvudkhan Suragan

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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.

Original language	English
Article number	127370
Journal	Applied Mathematics and Computation
Volume	432
DOIs	https://doi.org/10.1016/j.amc.2022.127370
Publication status	Published - Nov 1 2022

Funding

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 ).

Keywords

Caputo fractional derivative
Fixed point theory
Fractional differential equations
Mittag–Leffler functions
Riemann–Liouville fractional calculus
Series solutions

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2022.127370

Cite this

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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.",

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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

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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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JO - Applied Mathematics and Computation

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ER -

On linear fractional differential equations with variable coefficients

Abstract

Funding

Keywords

ASJC Scopus subject areas

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