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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 \(x'(t)=f(t,x(t)),\) \(t>0\), \(x(0)=0\).
Reviewer: H.Ade

MSC:

34A99 General theory for ordinary differential equations

Citations:

Zbl 0091.111
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