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.
Keywords:  finite fractional variation; weak $\sigma$-additive fractional; derivative; fractional impulsive equation; Dirac measure; Cauchy formula
Classification MSC:  26A45, 34A37
DOI:  10.21136/CMJ.2017.0455-15


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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

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