Czechoslovak Mathematical Journal, Vol. 67, No. 1, pp. 171-195, 2017
Functions of finite fractional variation and their applications to fractional impulsive equations
Dariusz Idczak
Received August 22, 2015. First published February 24, 2017.
Abstract: We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak $\sigma$-additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a $\sigma$-additive term - we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e.\^^Mequations containing the Dirac measures.
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Affiliations: Dariusz Idczak, Faculty of Mathematics and Computer Science, University of Lódź, Stefana Banacha 22, 90-238 Lódź, Poland, e-mail: idczak@math.uni.lodz.pl
