In this paper, we develop the theory of fractional hybrid differential equations involving Riemann-Liouville differential operators of order 0<q<1. An existence theorem for fractional hybrid differential equations is proved under mixed Lipschitz and Carathéodory conditions. Some fundamental fractional differential inequalities are also established which are utilized to prove the existence of extremal solutions. Necessary tools are considered and the comparison principle is proved which will be useful for further study of qualitative behavior of solutions. © 2011 Elsevier Ltd. All rights reserved.
Zhao, Y., Sun, S., Han, Z., & Li, Q. (2011). Theory of fractional hybrid differential equations. Computers and Mathematics with Applications, 62(3), 1312–1324. https://doi.org/10.1016/j.camwa.2011.03.041