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Behavior of solutions for a weighted Cauchy-type fractional differential problem. (English) Zbl 1131.26304
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:
26A33Fractional derivatives and integrals (real functions)
34K12Growth, boundedness, comparison of solutions of functional-differential equations