Theory of fractional hybrid differential equations ?
In this paper, we develop the theory of fractional hybrid differential equations involving RiemannLiouville differential operators of order 0<q<1 0 < q < 1 . An existence theorem for fractional hybrid differential equations is proved under mixed Lipschitz and Carathodory 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.
existence theorem fractional differential inequalities comparison principle