文章基本信息

标题：On applications of Caputo k -fractional derivatives
本地全文：下载
作者：Ghulam Farid ; Naveed Latif ; Matloob Anwar 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2019
卷号：2019
期号：1
页码：1-16
DOI：10.1186/s13662-019-2369-9
出版社：Hindawi Publishing Corporation
摘要：This research explores Caputo k-fractional integral inequalities for functions whose nth order derivatives are absolutely continuous and possess Grüss type variable bounds. Using Chebyshev inequality (Waheed et al. in IEEE Access 7:32137–32145, 2019) for Caputo k-fractional derivatives, several integral inequalities are derived. Further, Laplace transform of Caputo k-fractional derivative is presented and Caputo k-fractional derivative and Riemann–Liouville k-fractional integral of an extended generalized Mittag-Leffler function are calculated. Moreover, using the extended generalized Mittag-Leffler function, Caputo k-fractional differential equations are presented and their solutions are proposed by applying the Laplace transform technique.
关键词：Chebyshev inequality;k-Riemann;Liouville fractional integrals;Caputo fractional derivatives;Caputo k-fractional derivatives;Fractional differential equations