Geodesic
Functional-differential equations with Riemann-Liouville integrals in the nonlinearities
Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 587-595.

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A sufficient condition for the nonexistence of blowing-up solutions to evolution functional-differential equations in Banach spaces with the Riemann-Liouville integrals in their right-hand sides is proved. The linear part of such type of equations is an infinitesimal generator of a strongly continuous semigroup of linear bounded operators. The proof of the main result is based on a desingularization method applied by the author in his papers on integral inequalities with weakly singular kernels. The result is illustrated on an example of a scalar equation with one Riemann-Liouville integral.
DOI : 10.21136/MB.2014.144136
Classification : 34A08, 34G20, 34K05, 34K37
Keywords: fractional differential equation; Riemann-Liouville integral; blowing-up solution 
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Medveď, Milan. Functional-differential equations with Riemann-Liouville integrals in the nonlinearities. Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 587-595. doi : 10.21136/MB.2014.144136. http://geodesic.mathdoc.fr/articles/10.21136/MB.2014.144136/

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