Sign of the solutions of linear fractional differential equations and some applications

TL;DR

This paper explores the properties of solutions to linear fractional differential equations, emphasizing their signs, and applies these findings to fractional variational problems of Herglotz type, based on recent theoretical results.

Contribution

It extends recent theoretical results to analyze the sign of solutions and applies these insights to fractional variational problems of Herglotz type.

Findings

Characterization of solution signs for linear fractional differential equations

Application of theoretical results to fractional variational problems

Insights into nonlocal fractional dynamical systems

Abstract

In this work we wish to highlight some consequences of a recent result proved in [N. D. Cong and H. T. Tuan, Generation of nonlocal fractional dynamical systems by fractional differential equations, J. Integral Equations Appl. 29 (2017), no. 4, 585-608]. Particular emphasis will be given to its application on fractional variational problems of Herglotz type.