Нові типи систем N-арних інтегральних рівнянь: Автореф. дис… канд. фіз.- мат.наук / Г.О. Южакова, НАН України. Ін-т математики. — К., 1998. — 18 с.

IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO IAOAIAOEEE

THAEAEIAA Aaiia Ieaen??aia

OAeE 517.968

IIA? OEIE NENOAI N-A?IEO ?IOAA?AEUeIEO ??AIssIUe

01.01.02 — aeeoa?aioe?aeuei? ??aiyiiy

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Ee?a — 1998

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia ia eaoaae?? aeui? iaoaiaoeee ?1 Iaoe?iiaeueiiai
oaoi?/iiai oi?aa?neoaoo Oe?a?ie “Ee?anueeee iie?oaoi?/iee ?inoeooo”.

Iaoeiaee ea??aiee: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

A??/aiei I?ia Iiaian?aia, Iaoe?iiaeueiee oaoi?/iee oi?aa?neoao Oe?a?ie
“Ee?anueeee iie?oaoi?/iee ?inoeooo”, i?ioani? eaoaae?e aeui? iaoaiaoeee
?1.

Io?oe?ei? iiiiaioe:

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Aeouaiei Aiae??e A?naiiae/,
Iaoe?iiaeueiee oi?aa?neoao ?iai? Oa?ana Oaa/aiea, i?ioani? eaoaae?e
iaoaiaoe/ii? o?ceee;

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe Aaiaeay ?inoeneaa A?oae?eiae/,
?inoeooo aaco IAI Oe?a?ie, iaoeiaee ni?a?ia?oiee.

I?ia?aeia onoaiiaa:

Oa?e?anueeee aea?aeaaiee oi?aa?neoao, eaoaae?a iaoaiaoe/ii? o?ceee oa
ia/enethaaeueii? iaoaiaoeee, i. Oa?e?a.

Caoeno aeena?oaoe?? a?aeaoaeaoueny “ 26 ”. n?/iy 1999 ?ieo i 15 aiaeei?
ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.206.02 i?e ?inoeooo?
iaoaiaoeee IAI Oe?a?ie ca aae?anith:

252601, Ee?a-4, aoe. Oa?auaie?anueea, 3.

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? ?inoeoooo iaoaiaoeee
IAI Oe?a?ie (252601, Ee?a-4, aoe. Oa?auaie?anueea, 3).

Aaoi?aoa?ao ?ic?neaiee “ 23 ” a?oaeiy 1998?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee EO*EA A.TH.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. O aaaaoueio ?icae?eao iaoai?ee, cie?aia, a oai???
eiioaeoieo caaea/, oai??? o??uei, a oaeiae — o iaoaiaoe/i?e o?ceoe?, a
oai??? oaieii?ia?aeiino?, a oai??? aeaeo?inoaoeee, a oai??? aeeo?aeoe??
oa ?i. canoiniaothoueny oae caai? aeania ci?oai? e?aeia? caaea/?, ye?
yaeythoue niaith oe?ieee eean a?aie/ieo caaea/. Oea caaea/?, a yeeo
aeaeyae a?aie/ii? oiiae ci?ith?oueny a iaaeao iaei??? e o??? ae a?ai?
a?aieoe? iaeano?.

Iiaeia aeae?eeoe oae? iniiai? iaoiaee ?ica’ycaiiy aeania ci?oaieo
e?aeiaeo caaea/: iaoiaee oai??? ooieoe?e eiiieaenii? ci?iii?, iaoiae
?ioaa?aeueieo ia?aoai?aiue, iaoiae N-a?ieo (?ioaa?aeueieo aai
noiaoi?ieo) ??aiyiue, iaoiae i?oiaiiaeueieo iiiai/eai?a, aneiioioe/i?
iaoiaee, iaoiae ae?iaiaiai ?ioaa?i-aeeoa?aioe?thaaiiy, aa??aoe?ei?
iaoiaee, /enaeuei? iaoiaee oa ?i.

Cacia/eii, ui iaoiae N-a?ieo ?ioaa?aeueieo (noiaoi?ieo) ??aiyiue
aeyaeany iaeaoaeoeai?oei ?c no/anieo aiae?oe/ieo iaoiae?a ?ica’ycaiiy
aeania ci?oaieo e?aeiaeo caaea/. Oeae iaoiae oni?oii ?icaeaaany a
i?aoeyo A.E. Aa?aiyia, A.I. Aeaenaiae?iaa, A.A. Aiae??eeiaa,
A.A. Aaaaoea, I.I. A??/aiei, TH.A. Aaiaeaey, Ae.A. A?eeeoeueeiai,
A.O. A??i/aiea, A.?. Iinnaeianueeiai, A.A. Iaianthea, I.N. Ia?anthea,
A.ss. Iiiiaa, A.N. I?ioeaiea, A.O. Oe?oea, ss.N. Ooeyiaea, E. Beltrami,
W. Collins, J. Cooke, A. Erdelyi, S. Kalla, E. Love, B. Noble, M. Saigo,
I. Sneddon, K. Srivastava, C. Tranter oa ?i.

I?e ?ica’ycaii? aeineoue oe?ieiai eeano ci?oaieo a?aie/ieo caaea/, a
yeeo aeaeyae a?aie/ii? oiiae ci?ith?oueny aiaeii/an ia e?eueeio (aeaio,
o?ueio /e a?eueoa) a?aiyo a?aieoe? iaeano? aeieeathoue nenoaie ia?ieo,
iio??eieo, N-a?ieo ?ioaa?aeueieo ??aiyiue.

Caaaeueii? oai??? nenoai N-a?ieo ?ioaa?aeueieo ??aiyiue iiee ui ia
?nio?, yeithnue i??ith aea/ai? eeoa nenoaie N-a?ieo ?ioaa?aeueieo
??aiyiue c o?eaiiiiao?e/ieie ooieoe?yie oa ooieoe?yie Aannaey a yae?ao,
i?ei??ii, a ?iaioao A.I. ?ooiaoey, TH.I. Eocuei?ia, ss.N. Ooeyiaea,
G. Szefer, I. Lowndes, R. Westmann oa ?i. Oea iiaeia iiynieoe oei, ui
iiaoaeiaa caaaeueii? oai??? iia’ycaia c iiaeieaiiyi cia/ieo iaoaiaoe/ieo
o?oaeiiu?a, a ie??i oiai, oe? aeine?aeaeaiiy a iniiaiiio i?iaiaeeeenue
i?eeeaaeieeaie, yeeo a?eueoa oe?eaaeea eiino?oeoeaia oi?ia iiaoaeiae
?ica’yce?a.

*a?ac aaeeeo i?eeeaaeio aaaii?noue oa aoaeoeai?noue iaoiaeo N-a?ieo
?ioaa?aeueieo ??aiyiue oa ?o nenoai ?ica’ycaiiy naia iiaeo oei?a oaeiai
?iaeo nenoai oa aeine?aeaeaiiy ?o ?ica’yce?a ? oaae aaaeeeaith e
aeooaeueiith caaea/ath oni?oiiai aeei?enoaiiy oe??? aaeoc? oai???
?ioaa?aeueieo ??aiyiue.

Aeaia aeena?oaoe?y ye?ac i?iaeiaaeo? aeacaiee iai?yiie aeine?aeaeaiue ?
i?enay/aia ?ica’ycaiith oa aeine?aeaeaiith iiaeo oei?a nenoai N-a?ieo
?ioaa?aeueieo ??aiyiue.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie.

Aeena?oaoe?eia ?iaioa aeeiioaaeanue ia eaoaae?? aeui? iaoaiaoeee ?1 IOOO
“EI?” ca?aeii c eii?aeeiaoe?eiei ieaiii i??i?eoaoieo iai?yie?a ?icaeoeo
iaoee ? oaoi?ee I?i?noa?noaa ina?oe Oe?a?ie ii oai? “Aneiioioe/iee
aiae?c e?i?eieo nenoai oa ?o canoinoaaiiy” (?2858, 1995-1996 ??.).

Iaoa ?iaioe — iiaoaeiaa ?ica’yce?a oa aeine?aeaeaiiy oiia ?o ?nioaaiiy
aeey iiaeo oei?a nenoai N-a?ieo ?ioaa?aeueieo ??aiyiue neeaaei?oeo
eiino?oeoe?e.

Iaoiaeeea aeine?aeaeaiue. A ?iaio? aeei?enoai? aia?ao niaoe?aeueieo
ooieoe?e, oai??y ?ioaa?aeueieo ia?aoai?aiue, oai??y iia?aoi??a
ae?iaiaiai ?ioaa?oaaiiy, oai??y ?ioaa?aeueieo ??aiyiue, aeaiaioe oai???
iao?eoeue.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a:

— iaoiaeii ae?iaiaiai ?ioaa?oaaiiy ?ica’ycaii iia? oeie aeaiaei??ieo
nenoai ia?ieo oa iio??eieo ?ioaa?aeueieo ??aiyiue c ooieoe?yie Aannaey,
nenoai iio??eieo ?ioaa?aeueieo ??aiyiue c ooieoe?yie Aaoniia, ia?ieo
?ioaa?aeueieo ??aiyiue c i?e?aeiaieie ooieoe?yie Eaaeaiae?a oa c
H-ooieoe?yie Oiena;

— iaoiaeii aeiaecia/aiiy iaea?aeaii ?ica’ycee iiaeo oei?a nenoai ia?ieo
oa iio??eieo ?ioaa?aeueieo ??aiyiue c ocaaaeueiaieie i?e?aeiaieie
ooieoe?yie Eaaeaiae?a;

— iaoiaeii ?ioaa?aeueieo ia?aoai?aiue ?ica’ycaii iiaee oei nenoai ia?ieo
?ioaa?aeueieo ??aiyiue c ooieoe?yie A?ooaea?a;

— iaoiaeii i?aenoaiiaee ?ica’ycaii iiaee oei nenoai ia?ieo ?ioaa?aeueieo
??aiyiue, iia’ycaieo c ocaaaeueiaiei ?ioaa?aeueiei ia?aoai?aiiyi Aaaa?a;

— aeine?aeaeaii iniiai? aeanoeaino? eiiiiceoe?eieo ni?aa?aeiioaiue aeey
aeei?enoaieo iia?aoi??a ae?iaiaiai ?ioaa?oaaiiy;

— aeiaaaeaii ieceo oai?ai i?i oiiae ?nioaaiiy ?ica’yce?a aeuacacia/aieo
nenoai;

— iiaeaii i?eeeaaee i?aeoe/iiai canoinoaaiiy nenoai N-a?ieo
?ioaa?aeueieo ??aiyiue.

Oai?aoe/ia oa i?aeoe/ia oe?ii?noue ?iaioe. Aeena?oaoe?y ia? oai?aoe/iee
oa?aeoa? ? aiineoue aeeaae a caaaeueio oai??th nenoai ia?ieo, iio??eieo,
N-a?ieo ?ioaa?aeueieo ??aiyiue. ?? ?acoeueoaoe iiaeooue ciaeoe
canoinoaaiiy i?e ?ica’ycaii? eiie?aoieo i?eeeaaeieo caaea/ iaoaiaoe/ii?
o?ceee, iaoai?ee nooe?eueieo na?aaeiaeu, oai??? o?eueo?aoe?? oa ?i.

Ai?iaaoe?y ?iaioe. ?acoeueoaoe aeena?oaoe?eii? ?iaioe aeiiia?aeaeenue ?
iaaiai?thaaeenue ia 4-e, 5-e oa 7-e I?aeia?iaeieo iaoeiaeo eiioa?aioe?yo
?iai? aeaaeai?ea I. E?aa/oea (Ee?a, 1995, 1996, 1998 ??.), I?aeia?iaei?e
eiioa?aioe?? «Boundary value problems, special functions and fractional
calculus» (I?inuee, 1996 ?.), Oe?a?inuee?e eiioa?aioe?? «Iiaeaee?iaaiea
e enneaaeiaaiea onoie/eainoe nenoai» (Ee?a, 1996 ?.), 7-e iaoeia?e
I?aeaoc?anuee?e eiioa?aioe?? «Iaoaiaoe/aneia iiaeaee?iaaiea e e?aaaua
caaea/e» (Naia?a, 1997 ?.), I?aeia?iaei?e eiioa?aioe?? «Aneiioioe/i? oa
ye?ni? iaoiaee a oai??? iae?i?eieo eieeaaiue» (Ee?a, 1997 ?.),
I?aeaoc?anueeiio ia’?aeiaiiio iaoeiaiio nai?ia?? «Aeeoa?aioe?aeuei?
??aiyiiy oa ?o canoinoaaiiy» (Ee?a, 1997 ?.), a oeie?-nai?ia??
«Iae?i?ei? e?aeia? caaea/? iaoaiaoe/ii? o?ceee oa ?o canoinoaaiiy»
(Eai’yiaoeue-Iiae?euenueeee, 1996 ?.), ia can?aeaiiyo eaoaae?e aeui?
iaoaiaoeee N 1 Iaoe?iiaeueiiai oaoi?/iiai oi?aa?neoaoo Oe?a?ie «EI?»
(1995-1997 ??.).

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaai? a ?iaioao
[1]-[13]. O ?iaioao [4], [5] ? [11], iaienaieo o ni?aaaoi?noa? c
I. I. A??/aiei, iinoaiiaea caaea/ oa iaoeiaa ea??aieoeoai iaeaaeaoue
aeieoi?o o.-i. iaoe i?ioani?o I. I. A??/aiei, a iaea?aeaiiy eiie?aoieo
?acoeueoao?a oa ?o aeine?aeaeaiiy aeeiiai? iniaenoi aeena?oaioeith.
Nienie oeeo ?ia?o iiaeaii a e?ioe? aaoi?aoa?aoo.

No?oeoo?a oa ianya ?iaioe. ?iaioa ianyaii 135 noi??iie neeaaea?oueny c?
anooio, /ioe?ueio ?icae?e?a, aeniiae?a oa nieneo e?oa?aoo?e c 78
iaeiaioaaiue.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiaaii aea?? oaie aeena?oaoe?? ia iniia? aiae?co
no/aniiai noaio i?iaeaie, cacia/aii aeooaeuei?noue ? aaaeeea?noue
aeine?aeaeaiiy iiaeo oei?a nenoai N-a?ieo ?ioaa?aeueieo ??aiyiue,
ei?ioei aeeeaaeaii ci?no ?iaioe, iiaeaii caaaeueio oa?aeoa?enoeeo
iiaecie oa oai?aoe/ii? oe?iiino? iaea?aeaieo ?acoeueoao?a.

O ia?oiio ?icae?e? aeaii iaeyae iaoeiaeo aeine?aeaeaiue, aeecueeeo ca
iai?yieii aei oaie aeena?oaoe??.

O ae?oaiio ?icae?e? ?ica’ycaii aeaiaei??i? nenoaie ia?ieo oa iio??eieo
?ioaa?aeueieo ??aiyiue c ooieoe?yie Aannaey, nenoaie iio??eieo
?ioaa?aeueieo ??aiyiue c ooieoe?yie Aaoniia, ia?ieo ?ioaa?aeueieo
??aiyiue c ooieoe?yie A?ooaea?a, c’yniaaii oiiae ?nioaaiiy ?ica’yce?a.

Nenoaia c n N-a?ieo ?ioaa?aeueieo ??aiyiue ia? oaeee caaaeueiee
aeaeyae:

(1)

Aa?oi a?aecia/eoe, ui iaoiaee ?ica’ycaiiy oa aeine?aeaeaiiy nenoai
N-a?ieo ?ioaa?aeueieo ??aiyiue nooo?ai caeaaeaoue a?ae neeaaeo
niaoe?aeueieo ooieoe?e, ui aoiaeyoue aei neeaaeo yaea? oeeo ??aiyiue.
Na?aae oe?ieia?aeiieo iaoiae?a ?ica’ycaiiy oaeeo nenoai ne?ae iacaaoe
iaoiaee i?aenoaiiaee, aeiaecia/aiiy, iia?aoi??a ae?iaiaiai ?ioaa?oaaiiy,
?ioaa?aeueieo ia?aoai?aiue oa ?i. Iae/ano?oa ia i?aeoeoe?
canoiniaothoueny nenoaie ia?ieo (N=2) aai iio??eieo (N=3) ?ioaa?aeueieo
??aiyiue.

, oi nenoaio (1) iiaeia caienaoe a oaeiio iao?e/iiio aeaeyae?:

(2)

.

,

,

, aeaiaioe yeeo iathoue a?aeiia?aeii aeaeyae:

(3)

.

Aeey ?ica’ycaiiy iaea?aeaieo aeaiaei??ieo nenoai ia?ieo ?ioaa?aeueieo
??aiyiue c ooieoe?yie Aannaey a yae?ao canoiniaaii a?aeii? ocaaaeueiai?
iia?aoi?e ae?iaiaiai ?ioaa?i-aeeoa?aioe?thaaiiy:

ocaaaeueiaiee iia?aoi? Aaieaey

aeine?aeaeaii iniiai? aeanoeaino? oeeo ni?aa?aeiioaiue.

Oai?aia 2.1. Aeaiaei??ia nenoaia ia?ieo ?ioaa?aeueieo ??aiyiue aeaeyaeo

(4) ia? ?ica’ycie

— ae?aaiiaeuei? iao?eoe?, aeaiaioe yeeo caaeai? ni?aa?aeiioaiiyie

i?e oiiaao ia ia?aiao?e

.

(5)

Nenoaia aeaiaei??ieo iio??eieo ?ioaa?aeueieo ??aiyiue

(6)

,

,

— ae?eni? /enea ), ia ia?oee iiaeyae, iaei a?ae??ciy?oueny a?ae
nenoaie (4), aea iani?aaae? caaea/a iaaaaaoi oneeaaeieeanue ? iaea?aeaoe
?ica’ycie a caieiaiiio aeaeyae? ia aaea?oueny. Ni?aaaaeeeaa

Oai?aia 2.2. ?ica’ycaiiy aeaiaei??ii? nenoaie iio??eieo ?ioaa?aeueieo
??aiyiue (6) caiaeeoueny aei nenoaie ?ioaa?aeueieo ??aiyiue O?aaeaieueia
2-ai ?iaeo i?e oiiaao

,

,

.

Aeae? a oeueiio ae ?icae?e? ?icaeyiooi oae? nenoaie ia?ieo ?ioaa?aeueieo
??aiyiue:

(7)

caaeaia ni?aa?aeiioaiiyi

— aaia-ooieoe?y.

Oai?aia 2.3. ?ica’ycie nenoaie ia?ieo ?ioaa?aeueieo ??aiyiue (7) ia?
aeaeyae

(8)

ni?aaaaeeeaa ioe?iea

O e?ioe? ae?oaiai ?icae?eo ?icaeyiooi nenoaie iio??eieo ?ioaa?aeueieo
??aiyiue c ooieoe?yie Aaoniia a yae??:

(9)

— ocaaaeueiai? ?ioaa?aeuei? iia?aoi?e Aaieaey:

(10)

aecia/a?oueny ?ioaa?aeii

— ooieoe?y Aannaey 1-ai ?iaeo.

Oai?aia 2.4. ?ica’ycie nenoaie iio??eieo ?ioaa?aeueieo ??aiyiue (9)
caiaeeoueny aei nenoaie ?ioaa?aeueieo ??aiyiue O?aaeaieueia 2-ai ?iaeo
i?e oiiaao

I?e ?ica’ycaii? nenoaie (9) canoiniaaii iaoiae iia?aoi??a ae?iaiaiai
?ioaa?i-aeeoa?aioe?thaaiiy c aeaoaeueiei aeine?aeaeaiiyi iniiaieo
aeanoeainoae eiiiiceoe?e aeei?enoaieo iia?aoi??a.

, ia?ieo ?ioaa?aeueieo ??aiyiue c H-ooieoe?yie Oiena oa ia?ieo
?ioaa?aeueieo ??aiyiue, iia’ycaieo c ocaaaeueiaiei ?ioaa?aeueiei
ia?aoai?aiiyi Aaaa?a.

? ae?aaiiaeueiith. Oiae? ae?noa?ii nenoaio ia?ieo ?ioaa?aeueieo
??aiyiue c i?e?aeiaieie ooieoe?yie Eaaeaiae?a a yae?ao oaeiai aeaeyaeo:

(11)

aea

(12)

— iia?aoi? ocaaaeueiaiiai ?ioaa?aeueiiai ia?aoai?aiiy Iaea?a-Oiea.
Ni?aaaaeeeaa

ni?aaaaeeeaa ioe?iea

.

caaeaia ni?aa?aeiioaiiyi

(13)

O ?acoeueoao? iaea?aeo?ii nenoaio ia?ieo ?ioaa?aeueieo ??aiyiue c
ocaaaeueiaieie i?e?aeiaieie ooieoe?yie Eaaeaiae?a 1-iai ?iaeo a yae?ao:

(14)

— iia?aoi? ocaaaeueiaiiai ?ioaa?aeueiiai ia?aoai?aiiy Iaea?a-Oiea:

(15)

? iaeiei ?c ?ica’yce?a oaeiai ocaaaeueiaiiai aeeoa?aioe?aeueiiai
??aiyiiy Eaaeaiae?a:

. (16)

Ni?aaaaeeea?

ni?aaaeaeothoue oae? oiiae:

Oai?aia 3.3. ?ica’ycie nenoaie iio??eieo ?ioaa?aeueieo ??aiyiue aeaeyaeo

(17)

a?aeiia?aeii ni?aaaeaeothoue oiiae

Nenoaie (14) ? (17) ?ica’ycaii iaoiaeii aeiaecia/aiiy.

— H-ooieoe?? Oiena, aecia/ai? ieae/aiiaeaieie ae?acaie:

Iaea?aeeii nenoaio ia?ieo ?ioaa?aeueieo ??aiyiue c H-ooieoe?yie Oiena:

(19)

I?e oeueiio aeeiiothoueny oae? oiiae:

;

— eiiieaeni? /enea;

— aeiaeaoi? /enea;

;

;

i?ino?;

— ni?aaa;

;

.

(20)

Oai?aia 3.4. Nenoaia ia?ieo ?ioaa?aeueieo ??aiyiue (19) c H-ooieoe?yie
Oiena i?e oiiaao (20) ia? ?ica’ycie aeaeyaeo

(21)

.

Inoaii?ie a oeueiio ?icae?e? ?icaeyiooi nenoaie ia?ieo ?ioaa?aeueieo
??aiyiue, iia’ycaieo c ocaaaeueiaiei ?ioaa?aeueiei ia?aoai?aiiyi Aaaa?a:

— ocaaaeueiaia ooieoe?y Aaaa?a:

. (22)

O nenoai?

(23)

— ooeai?.

Oai?aia 3.5. ?ica’ycie nenoaie ia?ieo ?ioaa?aeueieo ??aiyiue (23)
caiaeeoueny aei ?ica’ycaiiy nenoaie ?ioaa?aeueieo ??aiyiue O?aaeaieueia
2-ai ?iaeo.

:

(24)

a iaeano?

ni?aaaeaeo? ??aiyiiy (24) a iaeano?

ni?aaaeaeothoue ieae/aiaaaaeai? e?aeia? oiiae:

?icae?eeaoe ci?ii? a ??aiyii? (24) ? aeei?enoaaoe aneiioioeeo
ocaaaeueiaieo i?e?aeiaieo ooieoe?e Eaaeaiae?a, caiaeeii iinoaaeaio
caaea/o aei ?ica’ycaiiy nenoaie ia?ieo ?ioaa?aeueieo ??aiyiue aeaeyaeo
(14).

AENIIAEE

O aeena?oaoe?ei?e ?iaio?, aeei?enoiaoth/e iaoiaee ae?iaiaiai
?ioaa?i-aeeoa?aioe?thaaiiy, aeiaecia/aiiy, ?ioaa?aeueieo ia?aoai?aiue,
i?aenoaiiaee, ?ica’ycaii oa aeine?aeaeaii iia? oeie nenoai N-a?ieo
?ioaa?aeueieo ??aiyiue c yae?aie neeaaei?oeo eiino?oeoe?e, a naia: c
yae?aie, ui i?noyoue ooieoe?? Aannaey, ooieoe?? Aaoniia, i?e?aeiai?
ooieoe?? Eaaeaiae?a 1-iai ?iaeo, ocaaaeueiai? i?e?aeiai? ooieoe??
Eaaeaiae?a 1-iai ?iaeo, ooieoe?? A?ooaea?a, H-ooieoe?? Oiena, c yae?aie,
ui iia’ycai? c ocaaaeueiaiei ia?aoai?aiiyi Aaaa?a. Anoaiiaeaii oai?aie
i?i oiiae ?nioaaiiy ?ica’yce?a oeeo nenoai. Aeey aeayeeo oei?a nenoai
N-a?ieo ?ioaa?aeueieo ??aiyiue ?icaeyiaii aeaiaei??iee aeiaaeie, ui
aeaco? ia ia?niaeoeai?noue iaea?aeaieo ?acoeueoao?a c iaoith ?icoe?aiiy
noa? ?o i?aeoe/iiai canoinoaaiiy.

Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaai? a ianooiieo ?iaioao:

1. THaeaeiaa A.I. Iia?aoi?iee iaoiae ?ica’ycaiiy aeaiaei??ii? nenoaie
iio??eieo ?ioaa?aeueieo ??aiyiue // Iaeeiaeiua e?aaaua caaea/e
iaoaiaoe/aneie oeceee e eo i?eeiaeaiey. Na. iao/i. o?. — Eeaa: Ei-o
iaoaiaoeee IAI Oe?aeiu.- 1996. — N. 287-289.

2. THaeaeiaa A.I. I?i iaeio aeaiaei??io nenoaio ia?ieo ?ioaa?aeueieo
??aiyiue // ?ioaa?. ia?aoai?aiiy oa ?o canoinoaaiiy aei e?aeiaeo caaea/:
Ca. iaoe. i?. — Ee?a: ?i-o iaoaiaoeee IAI Oe?a?ie. — 1996. — Aei. 11. —
N. 226-234.

3. Yuzhakova G.O. A system of the dual integral equations with the
generalized Legenlre’s functions // ?ioaa?. ia?aoai?aiiy oa ?o
canoinoaaiiy aei e?aeiaeo caaea/: Ca. iaoe. i?. — Ee?a: ?i-o iaoaiaoeee
IAI Oe?a?ie. — 1996.— Aei. 13.— N. 214-219.

4. A??/aiei I.I., THaeaeiaa A.I. Nenoaie N-a?ieo ?ioaa?aeueieo ??aiyiue
c ocaaaeueiaiith ooieoe??th Eaaeaiae?a // Aeiiia?ae? IAI Oe?a?ie.— 1997.
— ?8. — N. 20-25.

5. THaeaeiaa A.I. I?i nenoaie ia?ieo ?ioaa?aeueieo ??aiyiue, iia’ycaieo
c ocaaaeueiaiei ?ioaa?aeueiei ia?aoai?aiiyi Aaaa?a // Aeiiia?ae? IAI
Oe?a?ie.— 1998.—?11.— N. 52-55.

6. A??/aiei I.I., THaeaeiaa A.I. I?i aeaye? oeie nenoai ia?ieo
?ioaa?aeueieo ??aiyiue oa ?o i?aeoe/ia canoinoaaiiy a oai???
aeaeo?inoaoeee // Iaoeia? a?no? IOOO «EI?». — Ee?a. — 1998.— ?1. — N 92-
95.

7. THaeaeiaa A.A. Ia iaeiii i?eeiaeaiee iaiauaiiuo iia?aoi?ia ae?iaiiai
eioaa?e?iaaiey e ?aoaieth nenoai ia?iuo eioaa?aeueiuo o?aaiaiee //
O?oaeu Naaeueiie iao/iie iaaeaocianeie eiioa?aioeee «Iaoaiaoe/aneia
iiaeaee?iaaiea e e?aaaua caaea/e».— Naia?a.— 1997. — N. 91-94.

8. THaeaeiaa A.I. I?i aeayeo aeaiaei??io nenoaio ia?ieo ?ioaa?aeueieo
??aiyiue // Oace aeiiia?aeae *aoaa?oi? I?aeia?iaeii? iaoeiai?
eiioa?aioe?? ?i. aeaaeai?ea I. E?aa/oea. — Ee?a. — 1995. — N. 260.

9. THaeaeiaa A.I. Nenoaie ia?ieo ?ioaa?aeueieo ??aiyiue c ocaaaeueiaiith
ooieoe??th Aaoniia // Oace aeiiia?aeae I’yoi? I?aeia?iaeii? iaoeiai?
eiioa?aioe?? ?i. aeaaeai?ea I. E?aa/oea. — Ee?a. — 1996.— N. 504.

10. Yuzhakova A.A. On the system of the triple integral equations //
Internat. Conference «Boundary value problems, special functions and
fractional calculus».— Minsk. — 1996. — P. 168.

11. Yuzhakova G.O. On some applications of the generalized Mehler-Fock
integral transformation to solving of the system of the dual integral
equations // Oacenu aeieeaaeia Oe?aeineie eiioa?aioeee «Iiaeaee?iaaiea e
enneaaeiaaiea onoie/eainoe nenoai».— Eeaa. — 1996. — N. 150.

12. Virchenko N.O., Yuzhakova G.O. On one of the effective methods of
solving mixed problems of mathematical physics // «Aneiioioe/i? oa
ye?ni? iaoiaee a oai??? iae?i?eieo eieeaaiue». I?aeia?iaeia
eiioa?aioe?y. O?ao? Aiaietha?anuee? /eoaiiy. Oace aeiiia?aeae. — Ee?a:
?i-o iaoaiaoeee IAI Oe?a?ie. — 1997. — N. 192-193.

13. THaeaeiaa A.I. I?i aeanoeaino? aeayeeo iia?aoi??a ae?iaiaiai
?ioaa?oaaiiy oa ?o canoinoaaiiy i?e aeine?aeaeaii? ?ica’yce?a nenoai
N-a?ieo ?ioaa?aeueieo ??aiyiue // Nueiia I?aeia?iaeia iaoeiaa
eiioa?aioe?y ?i. aeaaeai?ea I. E?aa/oea. Iaoa??aee eiioa?aioe??.— Ee?a.
— 1998. — N.540.

THaeaeiaa A.I. Iia? oeie nenoai N-a?ieo ?ioaa?aeueieo ??aiyiue.

Aeena?oaoe?y ia caeiaoooy a/aiiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth: 01.01.02 —
aeeoa?aioe?aeuei? ??aiyiiy. ?inoeooo iaoaiaoeee IAI Oe?a?ie, Ee?a, 1998.

Caoeuathoueny ?acoeueoaoe oai?aoe/ieo aeine?aeaeaiue, aeeeaaeai? a
aeena?oaoe?? ? iioae?eiaai? a 13 ?iaioao.

Iiaoaeiaaii oa aeine?aeaeaii ?ica’ycee iiaeo oei?a nenoai N-a?ieo
?ioaa?aeueieo ??aiyiue c? neeaaeieie niaoe?aeueieie ooieoe?yie (Aaoniia,
A?ooaea?a, i?e?aeiaieie oa ocaaaeueiaieie i?e?aeiaieie Eaaeaiae?a 1-iai
?iaeo, H-ooieoe?yie Oiena oa ?i.), anoaiiaeaii aeinoaoi? oiiae ?nioaaiiy
iaea?aeaieo ?ica’yce?a. Aea/aii iniiai? aeanoeaino? eiiiiceoe?e
aeei?enoaieo iia?aoi??a ae?iaiaiai ?ioaa?i-aeeoa?aioe?thaaiiy. Iiaeaii
i?eeeaaee i?aeoe/iiai canoinoaaiiy ?icaeyiooeo nenoai N-a?ieo
?ioaa?aeueieo ??aiyiue.

Eeth/ia? neiaa: nenoaia N-a?ieo ?ioaa?aeueieo ??aiyiue, niaoe?aeuei?
ooieoe??, iia?aoi?e ae?iaiaiai ?ioaa?oaaiiy, ci?oaia e?aeiaa caaea/a.

THaeaeiaa A.A. Iiaua oeiu nenoai N-a?iuo eioaa?aeueiuo o?aaiaiee.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe: 01.01.02 —
aeeooa?aioeeaeueiua o?aaiaiey. Einoeooo iaoaiaoeee IAI Oe?aeiu, Eeaa,
1998.

Caueuathony ?acoeueoaou oai?aoe/aneeo enneaaeiaaiee, eceiaeaiiua a
aeenna?oaoeee e iioaeeeiaaiiua a 13 ?aaioao.

Iino?iaiu e enneaaeiaaiu ?aoaiey iiauo oeiia nenoai N-a?iuo
eioaa?aeueiuo o?aaiaiee ni neiaeiuie niaoeeaeueiuie ooieoeeyie (
Aaoniia, Oeooaea?a, i?eniaaeeiaiiuie e iaiauaiiuie i?eniaaeeiaiiuie
Eaaeaiae?a 1-iai ?iaea, H-ooieoeeyie Oiena e ae?. ). Onoaiiaeaiu
aeinoaoi/iua oneiaey nouanoaiaaiey iieo/aiiuo ?aoaiee. Eco/aiu iniiaiua
naienoaa eiiiiceoeee eniieueciaaiiuo iia?aoi?ia ae?iaiiai
eioaa?i-aeeooa?aioee?iaaiey. I?eaaaeaiu i?eia?u i?aeoe/aneiai i?eiaiaiey
?anniio?aiiuo nenoai N-a?iuo eioaa?aeueiuo o?aaiaiee.

Eeth/aaua neiaa: nenoaia N-a?iuo eioaa?aeueiuo o?aaiaiee, niaoeeaeueiua
ooieoeee, iia?aoi?u ae?iaiiai eioaa?e?iaaiey, niaoaiiay e?aaaay caaea/a.

Yuzhakova G.O. New types of the systems of N-ary integral equations.

Thesis for Ph. D. degree of physical and mathematical sciences on
speciality 01.01.02 — differential equations. Institute of Mathematics,
National Academy of Sciences of Ukraine, Kyiv, 1998.

The results of defended thesis were published in 13 papers.

Solutions of the different new types of the systems of N-ary integral
equations with the complex special functions (Watson’s, Whittaker’s,
associated and generalized associated Legendre’s of the 1-st kind, Fox’s
H-functions and others ) are constructed and investigated. The
sufficient conditions of the existence of obtained solutions are stated.
The main compositions properties of the used fractional integration
operators are studied. The examples of considered systems applying are
demonstrated.

Key words: system of N-ary integral equations, special functions,
fractional integration operators, mixed boundary value problem.

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