Analytical solution could be difficult to find, but numerical solutions are possible. See attached links. 

http://www.sciencedirect.com/science/article/pii/S0960077906005972

http://www.sciencedirect.com/science/article/pii/S0096300306004231

http://link.springer.com/article/10.1007/s10472-010-9222-x#/page-1

http://www.sciencedirect.com/science/article/pii/S0898122111001696

There's a tool in Maple to find particular solutions. Maple is really expensive, but a wonderful tool. You can probably get a student version.

You can pick up the specific function-solution, plug in fractional Riccatti equation and

find the  coefficients of Riccati equation.

Analytical Solutions of Riccati Fractional Equation with Coefficients Satisfying Differential Conditions with Arbitrary Function by Khaled K. Jaber

Exact Solution of Riccati Fractional Differential Equation by Khaled Jaber , Shadi Al -Tarawneh

I think the papers

http://www.hrpub.org/download/20160830/UJAM2-12607399.pdf

&

http://thescipub.com/pdf/10.3844/jmssp.2017.361.365

&

https://core.ac.uk/download/pdf/81180440.pdf

&

http://library.utia.cas.cz/separaty/2011/TR/kucera-0436431.pdf

&

https://www.sciencedirect.com/science/article/pii/S0898122111001696

are very useful.

With Best Wishes.@@

Article On the Solutions Fractional Riccati Differential Equation wi...