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Existence of the mild solution for fractional semilinear initial value problems. (English) Zbl 1160.34300
The authors study existence and uniqueness of mild solution for the semilinear initial value problems of non-integer order.

MSC:
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
26A33Fractional derivatives and integrals (real functions)
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Full Text: DOI
References:
[1] Barrett, J.: Differential equations of non-integer order, Canad. J. Math., No. 6, 529-541 (1954) · Zbl 0058.10702 · doi:10.4153/CJM-1954-058-2
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[3] Hadid, S. B.; Al-Shamani, J.: Liapunov stability of D.E. Of non-integer order, Arab. J. Maths 5, No. 1--2, 5-17 (1986)
[4] He, J. H.: Some applications of nonlinear fractional differential equations and their approximations, Bull. sci. Technol. 15, No. 2, 86-90 (1999)
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[6] Mainardi, F.: Fractional calculus ’some basic problems in continuum and statistical mechanics’, Fractals and fractional calculus in continuum mechanics, 291-348 (1997) · Zbl 0917.73004
[7] Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equations, (1993) · Zbl 0789.26002
[8] Podlubny, I.: Fractional differential equations, (1999) · Zbl 0924.34008
[9] Caputo, M.: Linear models of dissipation whose q is almost frequency independent, Part II, J. Ray, astr. Soc. 13, 529-539 (1967)