Existence and uniqueness theorems for sequential linear conformable fractional differential equations. (English) Zbl 1389.34012

Gökdoğan, Ahmet; Ünal, Emrah; Çelík, Ercan

Miskolc Math. Notes 17, No. 1, 267-279 (2016).

Summary: Recently, a new definition of fractional derivative called the “conformable fractional derivative” which is based on limits was introduced by R. Khalil et al. [J. Comput. Appl. Math. 264, 65–70 (2014; Zbl 1297.26013)]. Later, T. Abdeljawad [ibid. 279, 57–66 (2015; Zbl 1304.26004)] improved these definitions and gave the basic concepts in this new fractional calculus. In this paper, we generalize Abel’s formula and Wronskian determinant definition and establish existence and uniqueness theorems for sequential linear conformable fractional differential equations.

MSC:

34A08	Fractional ordinary differential equations
34A30	Linear ordinary differential equations and systems

Keywords:

sequential linear fractional differential equations; conformable fractional derivative; existence and uniqueness theorems

Citations:

Zbl 1297.26013; Zbl 1304.26004