Geodesic
Functions of finite fractional variation and their applications to fractional impulsive equations
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 171-195.

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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. equations containing the Dirac measures.
DOI : 10.21136/CMJ.2017.0455-15
Classification : 26A45, 34A37
Keywords: finite fractional variation; weak $\sigma $-additive fractional; derivative; fractional impulsive equation; Dirac measure; Cauchy formula 
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Idczak, Dariusz. Functions of finite fractional variation and their applications to fractional impulsive equations. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 171-195. doi : 10.21136/CMJ.2017.0455-15. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0455-15/

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