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On the fractional differential equations. (English) Zbl 0757.34005
The author deals with the semilinear differential equation d α x(t)/dt α =f(t,x(t)), t>0, where α is any positive real number. In [Kyungpook Math. J. 28, No. 2, 119-122 (1988; Zbl 0709.34011)] the author has proved the existence, uniqueness, and some properties of the solution of this equation when 0<α<1. Here he mainly studies (besides the other properties) the continuation of the solution of this equation to the solution of the corresponding initial value problem when [α]=k, k=1,2,3,. Applications of singular integro- differential equations are considered.

MSC:
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
26A33Fractional derivatives and integrals (real functions)