On applications of Caputo k-fractional derivatives-Reference-Cited by-同舟云学术

On applications of Caputo k-fractional derivatives

Published:2019-10-16 Issue:1 Volume:2019 Page:
ISSN:1687-1847
Container-title:Advances in Difference Equations
language:en
Short-container-title:Adv Differ Equ

Author:

Farid Ghulam,Latif Naveed,Anwar Matloob,Imran Ali,Ozair Muhammad,Nawaz Madeeha

Abstract

Abstract 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.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Link

http://link.springer.com/content/pdf/10.1186/s13662-019-2369-9.pdf

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