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On the fractional differential equations. (English) Zbl 0757.34005
The author deals with the semilinear differential equation $d\sp \alpha x(t)/dt\sp \alpha=f(t,x(t))$, $t>0$, where $\alpha$ 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 $0<\alpha<1$. 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 $[\alpha]=k$, $k=1,2,3,\dots\ $. Applications of singular integro- differential equations are considered.

34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
26A33Fractional derivatives and integrals (real functions)
Full Text: DOI
[1] Apostol, T. M.: 2nd ed. Mathematical analysis. Mathematical analysis (1974)
[2] Curtain, R. F.; Prichard, A. J.: Functional analysis in modern applied mathematics A.P.. (1977)
[3] El-Sayed, A. M. A.: Fractional differential equations. Kyungpook math. J. 28, No. 2 (1988) · Zbl 0709.34011
[4] Gelfand, I. M.; Shilov, G. E.: Generalized functions. (1958) · Zbl 0091.11103
[5] Shilove, G. E.: Generalized functions and partial differential equations. Mathematics and its applications (1968)