## Fractional differential equations.(English)Zbl 0709.34011

The author considers the differential equation $$d^{\alpha}x/dt^{\alpha}=f(t,x(t)),$$ $$t>0$$, $$0<\alpha <1$$ with fractional derivatives according to I. M. Gelfand and G. F. Shilov [Generalized functions, Vol. 1 (1959; Zbl 0091.111)]. He examines the concept of solution of the above equation, its existence, uniqueness and coincidence with the solution of the initial value problem $$x'(t)=f(t,x(t)),$$ $$t>0$$, $$x(0)=0$$.