Chapter 8, P.5o of Book "Integrals and derivatives of fractional order, and some applications" (Page 610) is devoted to the application of fractional differentiation to integration of differential equations of the whole order. However, this book is in Russian. [Самко С.Г., Кильбас А.А., Маричев О.И. Интегралы и производные дробного порядка и некоторые их приложения. 1987], for example, http://rutracker.org/forum/viewtopic.php?t=2637903
I believe that in your University or at the nearby University you can find mathematician from Azerbaijan. I hope they will help you understand 4 main pages. Please, download next pdf-file and see page 610-613: