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Axioms 2018, 7(3), 55; https://doi.org/10.3390/axioms7030055

Conformable Laplace Transform of Fractional Differential Equations

1
Department of Exact and Technological Sciences, State University of Southwest Bahia, Vitória da Conquista, BA 45083-900, Brazil
2
Centro Universitário SENAI CIMATEC, Salvador, BA 41650-010, Brazil
*
Author to whom correspondence should be addressed.
Received: 30 June 2018 / Revised: 31 July 2018 / Accepted: 4 August 2018 / Published: 7 August 2018
(This article belongs to the Special Issue Fractional Differential Equations)
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Abstract

In this paper, we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, the analytical solution for a class of fractional models associated with the logistic model, the von Foerster model and the Bertalanffy model is presented graphically for various fractional orders. The solution of the corresponding classical model is recovered as a particular case. View Full-Text
Keywords: fractional differential equations; conformable derivative; Bernoulli equation; exact solution fractional differential equations; conformable derivative; Bernoulli equation; exact solution
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Silva, F.S.; Moreira, D.M.; Moret, M.A. Conformable Laplace Transform of Fractional Differential Equations. Axioms 2018, 7, 55.

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