Functions of finite fractional variation and their applications to fractional impulsive equations

Dariusz Idczak

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 1, page 171-195
  • ISSN: 0011-4642

Abstract

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We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak σ -additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a σ -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.

How to cite

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Idczak, Dariusz. "Functions of finite fractional variation and their applications to fractional impulsive equations." Czechoslovak Mathematical Journal 67.1 (2017): 171-195. <http://eudml.org/doc/287928>.

@article{Idczak2017,
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. equations containing the Dirac measures.},
author = {Idczak, Dariusz},
journal = {Czechoslovak Mathematical Journal},
keywords = {finite fractional variation; weak $\sigma $-additive fractional; derivative; fractional impulsive equation; Dirac measure; Cauchy formula; distributional derivatives; locally finite variation; impulsive hyperbolic equation},
language = {eng},
number = {1},
pages = {171-195},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Functions of finite fractional variation and their applications to fractional impulsive equations},
url = {http://eudml.org/doc/287928},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Idczak, Dariusz
TI - Functions of finite fractional variation and their applications to fractional impulsive equations
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 1
SP - 171
EP - 195
AB - 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.
LA - eng
KW - finite fractional variation; weak $\sigma $-additive fractional; derivative; fractional impulsive equation; Dirac measure; Cauchy formula; distributional derivatives; locally finite variation; impulsive hyperbolic equation
UR - http://eudml.org/doc/287928
ER -

References

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