Abstract
This note is motivated by some papers treating the fractional hybrid differential equations involving Riemann-Liouville differential operators of order $0 < \alpha< 1 $ . An existence theorem for this equation is proved under mixed Lipschitz and Caratheodory conditions. 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 is proved, which will be useful for further study of qualitative behavior of solutions.
Highlights
During the past decades, fractional differential equations have attracted many authors
There have been many works on the theory of hybrid differential equations, and we refer the readers to the articles [ – ]
The authors of [ ] established the existence theorem for fractional hybrid differential equations and some fundamental differential inequalities, they established the existence of extremal solutions
Summary
Fractional differential equations have attracted many authors (see [ – ]). The authors of [ ] established the existence theorem for fractional hybrid differential equations and some fundamental differential inequalities, they established the existence of extremal solutions. We develop the theory of boundary fractional hybrid differential equations involving Caputo differential operators of order < α
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