AN INTEGRO-DIFFERENTIAL EQUATION OF VOLTERRA TYPE WITH SUMUDU TRANSFORM
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1 Mmic A Vol o AN INTGRO-IRNTIAL QUATION O VOLTRRA TYP WITH UMUU TRANORM R Ji cool o Mmic d Allid cic Jiwji Uiviy Gwlio-474 Idi mil - ji3@dimil.com i ig pm o Applid Mmic Ii o Tcology d Mgm Gwlio-474 Idi mil - di26_om@yoo.co.i Abc I i pp clod om olio o ciol igo-diil qio o Vol yp ivolvig Mig-Ll cio b obid ig ig owd ciq o md om. om picl c v lo b coidd. Ky wod: Igo-diil qio o Vol yp md om Rim-Liovill ciol igl d diil. Mmic bjc Cliicio 2: 26A33 47Gxx 455.
2 542 R Ji d i ig. INTROUCTION T diil qio v plyd cl ol i vy pc o pplid mmic o vy log im d v md g igiicc wi dv o comp d dvcd ow. T vl om wic d o olv diil qio iig i giig poblm. T icld Lplc Mlli oi d ciol oi om c. Rcly w igl om ow md om b iodcd by Wgl ]. o i cl d i pvig popi md om g poil o pplicbiliy i o giig mmic d pplid cic. ic i iodcio vl c dvod o xplo i popi d i popciv. Coidd oicl dl o Lplc om i povid mo civ ool o poblm olvig wio oig o w qcy domi. T iv md om w giv by Woo 2]. vl dml popi o md om w divd by Blgcm l 2 3]. Ty lo pplid i om o olv igl podcio poblm. L o Loo d Bji 6] obid olio o Abl igl qio ig md om. T objc o i pp i o p om o impo o md om d igowd liv divio o olio o ciol igo-diil qio o Vol yp. T olio o ciol igo-diil qio i dmod by my o icldig B ] Ro d cdv 8] Kilb igo d x 5] Gp d m 4] d x 9] d o. 2. INITION T md om c b did 4 6] o cio o xpoil od ollow: W coid cio i A did i om: / j 2 j A M d/o c M i -... o giv cio i A co M m b ii wil τ d τ 2 d o imloly xi d c my b iii. Id o big d pow o xpoil i c o Lplc om vibl i md om i d o co vibl i gm o cio. pciiclly o md om i did by G : ] d d
3 I o wod md om c b wi ] : G 2 / d... 3 T covolio o md om i ] ] * G g g w R > 4 T ivio oml o md om i giv by i i d G i 2 /... 5 T glid Mig-Ll cio i pm α β δ i did by Pb 7 ]! 6 wic i pcil c o β = ρ = dc o wll-ow Mig-Ll cio. T Rim-Liovill ciol igl o od i did i ollowig om: - d w R > 7 imilly Rim-Liovill ciol diviv o od i did i ollowig om: ] - d d d w Rη > 8 T md om o ciol diviv o cio i did 2 4] ] ] ; H 9 md om o Mig-Ll cio i giv by ] - d 3. OLUTION O INTGRO-IRNTIAL QUATION Vio pyicl pom li diio c b modld i m o igo-diil qio. T c b xdd o ciol igl qio by plcig odiy igl o i ciol co p. Coid A Igo-iil qio o Vol Typ 543
4 Vol yp igo-diil ivolvig glid Mig-Ll cio d olv by mployig md om. Tom : L ρ Є C d Є R R > R > b md o b coio o vy ii ivl T] < < d b o xpoil od σ w.t Ccy poblm o ciol igo-diil qio o Vol yp ] d og wi iiil codiio ] =. = --R] -< ] Є N 2 w pcibd co xi iq coio olio o Ccy poblm d 2 giv by d 3 w 4 d 5 Poo: By pplyig md om o qio w g H - H wic giv - H 7 By ig iv md om w g H Now pplyig covolio om o md om d R Ji d i ig
5 w Ω d Θτ i giv by qio 4 d 5 pcivly. PCIAL CA: i By ig ρ = i w g ] d 9 Ud lv codiio iq coio olio i giv by d 2 w 2 d 22 ii By ig ρ = d β = i Mig-Ll cio w v 23 ] d 24 T iq coio olio d lv codiio i giv by d 25 w 26 d A Igo-iil qio o Vol Typ 545
6 27 Tom 2: I ρ λ Є C d Є R R > R > d i md o b coio o vy ii ivl T] < < d i o xpoil od σ w Vol yp igl qio ] d 28 i xplici olio d 29 w 3 Poo: By pplyig md om o bo id o Vol igl qio 28 w g H H - 3 d c H 32 By ig iv md om w g - - H By pplicio o covolio om o md om w g d 33 w Θτ i giv by qio 3. I i opd ciq d i i cp will b pplicbl o wid g o icldig giig mmicl cmicl d pyicl cic i viw o q occc o c igo-diil qio i bjc. RRNC 546 R Ji d i ig
7 A Igo-iil qio o Vol Typ 547 ] J. H. B iil qio o o ig od Cd. J. M ]. B. M. Blgcm A. A. Kblli d. L. Kll Alyicl ivigio o md om d pplicio o igl qio Hidwi Pb. Cop. Mmicl Pob. i gg ]. B. M. Blgcm d A. A. Kblli md om dml popi ivigio d pplicio Hidwi Pb. Cop. I. J. o Appl. M. d ocic Al ] V. G. Gp d B. m A olio o ciol Vol yp igo diil qio ocid wi Loo d Hly cio Globl J. ci. oi Rc Vol ] A. A. Kilb M. igo d R. K. x olio o Vol igo diil qio wi glid Mig-Ll cio i l J. Igl q. d Appl. Vol. 4 No ]. Loo d P. K. Bji O olio o diibiol Abl igl qio by diibiol md om Hidwi Pb. Cop. I. J. o M. d Mmicl cic ] T. R. Pb A igl igl qio wi glid Mig- Ll cio i l Yoom M. J ] B. Ro d B. cdv T olio o ci igl qio by m o opo o biy od Am. M. Moly ] R. K. x Aliv divio o olio o ci igodiil qio o Vol yp Gi d Vol ] R. K. x d M. igo Ci popi o ciol opo ocid wi glid Mig-Ll cio I. J. o Toy d Appl. CAA ] G. K. Wgl md om: w igl om o olv diil qio i cool giig poblm I. J. M. dc. ci. Tcol ]. Woo Applicio o md om o pil diil qio I. J. o Mmicl d. i ci. d Tcology 25 No Rcivd: My 22
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