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arXiv · 1809.02189

Global Solution to a Nonlinear Fractional Differential Equation for the Caputo-Fabrizio Derivative

Sabrina Roscani·Domingo Tarzia·Lucas Venturato
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Abstract

This paper deals with the fractional Caputo--Fabrizio derivative and some basic properties related. A computation of this fractional derivative to power functions is given in terms of Mittag--Lefler functions. The inverse operator named the fractional Integral of Caputo--Fabrizio is also analyzed. The main result consists in the proof of existence and uniqueness of a global solution to a nonlinear fractional differential equation, which has been solved previously for short times by Lozada and Nieto (Progr. Fract. Differ. Appl., 1(2):87--92, 2015). The effects of memory as well as the convergence of the obtained results when $\al \nearrow 1$ (and the classical first derivative is recovered) are analyzed throughout the paper.

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Sabrina Roscani, Domingo Tarzia, Lucas Venturato. 2018-09-06. Global Solution to a Nonlinear Fractional Differential Equation for the Caputo-Fabrizio Derivative. https://arxiv.org/abs/1809.02189

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