On conformable fractional calculus

• Published in: Journal of computational and applied mathematics Vol. 279; pp. 57 - 66
• Main Author: Abdeljawad, Thabet
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2015
• Subjects: Chain rule; Fractional exponential function; Fractional Gronwall’s inequality; Fractional Taylor power series expansion; Left and right conformable fractional derivatives; Left and right conformable fractional integrals; Chain rule; Fractional exponential function; Left and right conformable fractional derivatives; Left and right conformable fractional integrals; Fractional Taylor power series expansion; Fractional Gronwall’s inequality
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2014.10.016

Recently, the authors Khalil et al. (2014) introduced a new simple well-behaved definition of the fractional derivative called conformable fractional derivative. In this article we proceed on to develop the definitions there and set the basic concepts in this new simple interesting fractional calculus. The fractional versions of chain rule, exponential functions, Gronwall’s inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed.