Behavior of solutions for a weighted Cauchy-type fractional differential problem. (English) Zbl 1131.26304

Furati, Khaled M.; Tatar, Nasser-eddine

J. Fractional Calc. 28, 23-42 (2005).

Summary: We investigate the behavior of solutions of a fractional differential problem. Namely, we consider a weighted Cauchy-type problem involving a fractional derivative in the sense of Riemann-Liouville and a non-local term. In contrast to the case where we may have blow up in finite time, for certain nonlinearities, we show that solutions decay as a power type function on some intervals which could be very large.

MSC:

26A33	Fractional derivatives and integrals
34K12	Growth, boundedness, comparison of solutions to functional-differential equations