Research
Theory of fractional hybrid differential equations with linear perturbations of second type
School of Mathematical Sciences, University of Jinan, Jinan, Shandong, 250022, P.R. China
Boundary Value Problems 2013, 2013:23 doi:10.1186/1687-2770-2013-23
Published: 11 February 2013Abstract
In this paper, we develop the theory of fractional hybrid differential equations with
linear perturbations of second type involving Riemann-Liouville differential operators
of order 
. An existence theorem for fractional hybrid differential equations is proved under
the φ-Lipschitz condition. Some fundamental fractional differential inequalities which
are utilized to prove the existence of extremal solutions are also established. Necessary
tools are considered and the comparison principle which will be useful for further
study of qualitative behavior of solutions is proved.
MSC: 34A40, 34A12, 34A99.
