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1 2023

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On some conformable boundary value problems in the setting of a new generalized conformable fractional derivative

Vivas-Cortez Miguel, Árciga Martin Patricio, Najera Juan Carlos, Hernández Jorge Eliecer

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220212

The fundamental objective of this article is to investigate about the boundary value problem with the uses of a generalized conformable fractional derivative introduced by Zarikaya et al. (On generalized the conformable calculus, TWMS J. App. Eng. Math. 9 (2019), no. 4, 792–799, http://jaem.isikun.edu.tr/web/images/articles/vol.9.no.4/11.pdf). In the development of the this article, by using classical methods of fractional calculus, we find a definition of the generalized fractional Wronskian according to the fractional differential operator defined by Zarikaya, a fractional version of the Sturm-Picone theorem, and in addition, the stability criterion given by the Hyers-Ulam theorem is studied with the use of the aforementioned fractional derivatives.