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.


34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26A33 Fractional derivatives and integrals
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[1] Barrett, J., Differential equations of non-integer order, Canad. J. Math., 6, 529-541 (1954) · Zbl 0058.10702
[2] Delbosco, D.; Rodino, L., Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl., 204, 609-625 (1996) · Zbl 0881.34005
[3] Hadid, S. B.; Al-shamani, J., Liapunov stability of D.E. of non-integer order, Arab. J. Maths, 5, 1-2, 5-17 (1986) · Zbl 0659.34056
[4] He, J. H., Some applications of nonlinear fractional differential equations and their approximations, Bull. Sci. Technol., 15, 2, 86-90 (1999)
[5] He, J. H., Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Engrg., 167, 57-68 (1998) · Zbl 0942.76077
[6] Mainardi, F., Fractional calculus ‘Some basic problems in continuum and statistical mechanics’, (Carpinteri, A.; Mainardi, F., Fractals and Fractional calculus in Continuum Mechanics (1997), Springer-Verlag: Springer-Verlag New York), 291-348 · Zbl 0917.73004
[7] Miller, K. S.; Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), John Wiley and Sons, Inc.: John Wiley and Sons, Inc. New York · Zbl 0789.26002
[8] Podlubny, I., Fractional Differential Equations (1999), Academic Press: Academic Press New York · Zbl 0918.34010
[9] Caputo, M., Linear models of dissipation whose q is almost frequency independent, Part II, J. Ray, Astr. Soc., 13, 529-539 (1967)
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