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Zbl 0757.34005
El-Sayed, A.M.A.
On the fractional differential equations.
(English)
[J] Appl. Math. Comput. 49, No.2-3, 205-213 (1992). ISSN 0096-3003

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.
[S.D.Bajpai (Isa Town)]
MSC 2000:
*34A12 Initial value problems for ODE
26A33 Fractional derivatives and integrals (real functions)

Keywords: semilinear differential equation; continuation; initial value problem; singular integro-differential equations

Citations: Zbl 0709.34011

Cited in: Zbl 0895.34003

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