id sid eid entity type iajs-1821 1 1 microsoft ORG iajs-1821 1 2 490 CARDINAL iajs-1821 1 3 2017 CARDINAL iajs-1821 1 4 al-haitham ORG iajs-1821 1 5 10.30526/2017.ihsciconf.1821 CARDINAL iajs-1821 1 6 http://www.ihsciconf.org/conf/ PERSON iajs-1821 1 7 www.ihsciconf.org CARDINAL iajs-1821 1 8 fredholm-integro ORG iajs-1821 1 9 abdul khaleq PERSON iajs-1821 1 10 o. al-jubory PERSON iajs-1821 2 1 mathematics/ college of science ORG iajs-1821 2 2 hussain salih PERSON iajs-1821 3 1 university of technology ORG iajs-1821 3 2 second ORDINAL iajs-1821 4 1 petrov-galerkian PERSON iajs-1821 4 2 pgm ORG iajs-1821 5 1 pgm ORG iajs-1821 6 1 matlab10. ORG iajs-1821 7 1 petrov-galerkian PERSON iajs-1821 8 1 2017 CARDINAL iajs-1821 8 2 al-haitham ORG iajs-1821 8 3 10.30526/2017.ihsciconf.1821 CARDINAL iajs-1821 8 4 http://www.ihsciconf.org/conf/ PERSON iajs-1821 8 5 1.introduction CARDINAL iajs-1821 9 1 linear ORG iajs-1821 14 1 fractional integro-differential ORG iajs-1821 14 2 second ORDINAL iajs-1821 15 1 z. taheri PERSON iajs-1821 15 2 javadi PERSON iajs-1821 15 3 e. babolian PERSON iajs-1821 16 1 1 CARDINAL iajs-1821 16 2 legendre ORG iajs-1821 17 1 2 CARDINAL iajs-1821 17 2 bernstein PERSON iajs-1821 18 1 asma a. PERSON iajs-1821 18 2 adem kΔ±lΔ±c ORG iajs-1821 18 3 bachok m. PERSON iajs-1821 19 1 3 CARDINAL iajs-1821 20 1 li huanga PERSON iajs-1821 20 2 xianfang li PERSON iajs-1821 20 3 yulin zhaoa PERSON iajs-1821 20 4 xiang-yang PERSON iajs-1821 21 1 4 CARDINAL iajs-1821 21 2 taylor series PERSON iajs-1821 22 1 peter linzt PERSON iajs-1821 23 1 5 CARDINAL iajs-1821 23 2 nystrom GPE iajs-1821 23 3 linear integro- ORG iajs-1821 25 1 0 𝛿 𝑛 MONEY iajs-1821 25 2 1.b CARDINAL iajs-1821 26 1 2. CARDINAL iajs-1821 26 2 definition1 PERSON iajs-1821 26 3 0 CARDINAL iajs-1821 28 1 t h (t ORG iajs-1821 29 1 1 CARDINAL iajs-1821 31 1 1 CARDINAL iajs-1821 31 2 0 DATE iajs-1821 32 1 f(x ORG iajs-1821 32 2 2017 CARDINAL iajs-1821 32 3 al-haitham ORG iajs-1821 32 4 10.30526/2017.ihsciconf.1821 CARDINAL iajs-1821 32 5 http://www.ihsciconf.org/conf/ PERSON iajs-1821 33 1 1 𝛼 QUANTITY iajs-1821 33 2 1 CARDINAL iajs-1821 35 1 0 DATE iajs-1821 35 2 0 2 CARDINAL iajs-1821 37 1 0 CARDINAL iajs-1821 37 2 1 CARDINAL iajs-1821 37 3 0 3 DATE iajs-1821 39 1 0 CARDINAL iajs-1821 39 2 1 𝛼 π‘š QUANTITY iajs-1821 39 3 4 CARDINAL iajs-1821 40 1 0 CARDINAL iajs-1821 40 2 1 𝛼 π‘š QUANTITY iajs-1821 40 3 5 CARDINAL iajs-1821 41 1 2.1 CARDINAL iajs-1821 41 2 bernstein PERSON iajs-1821 42 1 1 CARDINAL iajs-1821 44 1 0,1,2 DATE iajs-1821 44 2 bernstein PERSON iajs-1821 44 3 bernstein ORG iajs-1821 45 1 0 ≀ MONEY iajs-1821 45 2 6 CARDINAL iajs-1821 45 3 four CARDINAL iajs-1821 45 4 bernstein ORG iajs-1821 45 5 1 CARDINAL iajs-1821 46 1 6x CARDINAL iajs-1821 46 2 1 CARDINAL iajs-1821 46 3 11 15π‘₯ 1 DATE iajs-1821 46 4 6π‘₯ 1 CARDINAL iajs-1821 46 5 1 CARDINAL iajs-1821 46 6 20π‘₯ 1 DATE iajs-1821 46 7 1 CARDINAL iajs-1821 46 8 1 CARDINAL iajs-1821 46 9 40 CARDINAL iajs-1821 46 10 1 CARDINAL iajs-1821 46 11 1 CARDINAL iajs-1821 46 12 1 CARDINAL iajs-1821 46 13 1 CARDINAL iajs-1821 46 14 60π‘₯ 1 DATE iajs-1821 46 15 30π‘₯ 1 DATE iajs-1821 46 16 1 CARDINAL iajs-1821 46 17 1 CARDINAL iajs-1821 46 18 7 CARDINAL iajs-1821 46 19 18π‘₯ 1 DATE iajs-1821 46 20 75 CARDINAL iajs-1821 46 21 1 CARDINAL iajs-1821 46 22 45π‘₯ 1 DATE iajs-1821 46 23 6π‘₯ 1 CARDINAL iajs-1821 46 24 1 CARDINAL iajs-1821 46 25 2017 CARDINAL iajs-1821 46 26 al-haitham ORG iajs-1821 46 27 10.30526/2017.ihsciconf.1821 CARDINAL iajs-1821 46 28 http://www.ihsciconf.org/conf/ PERSON iajs-1821 46 29 www.ihsciconf.org CARDINAL iajs-1821 46 30 3 CARDINAL iajs-1821 46 31 pgm ORG iajs-1821 46 32 pgm ORG iajs-1821 47 1 2 CARDINAL iajs-1821 49 1 2 CARDINAL iajs-1821 52 1 π·βˆ— 𝑒 𝐾𝑒 PERSON iajs-1821 52 2 ∈ ORG iajs-1821 52 3 2 CARDINAL iajs-1821 53 1 pgm ORG iajs-1821 54 1 petrov-galerkin PERSON iajs-1821 54 2 pgm ORG iajs-1821 55 1 𝑋 βŠ‚ x ORG iajs-1821 55 2 π‘Œ βŠ‚ ORG iajs-1821 57 1 0 CARDINAL iajs-1821 57 2 n β†’ ∞. ORG iajs-1821 57 3 ∈ ORG iajs-1821 57 4 yn ORG iajs-1821 57 5 〈 f PERSON iajs-1821 57 6 3 CARDINAL iajs-1821 58 1 ∈ ORG iajs-1821 58 2 〈x ⎯ PERSON iajs-1821 58 3 4 CARDINAL iajs-1821 58 4 ∈ ORG iajs-1821 59 1 ∈ ORG iajs-1821 61 1 y n ∩ 𝑋 PERSON iajs-1821 61 2 0 CARDINAL iajs-1821 61 3 5 CARDINAL iajs-1821 61 4 ∏ 𝑋 = π‘Œ ORG iajs-1821 63 1 ∈ ORG iajs-1821 64 1 ∈ ORG iajs-1821 64 2 β€–π‘₯ 𝑄 PRODUCT iajs-1821 65 1 2017 CARDINAL iajs-1821 65 2 al-haitham ORG iajs-1821 65 3 10.30526/2017.ihsciconf.1821 CARDINAL iajs-1821 65 4 http://www.ihsciconf.org/conf/ PERSON iajs-1821 65 5 www.ihsciconf.org CARDINAL iajs-1821 66 1 1 CARDINAL iajs-1821 66 2 ∈ ORG iajs-1821 66 3 2 CARDINAL iajs-1821 67 1 1,2 CARDINAL iajs-1821 67 2 3 CARDINAL iajs-1821 67 3 ∏ 𝑋 = π‘Œ ORG iajs-1821 68 1 3 CARDINAL iajs-1821 69 1 βŒ©π·βˆ— 𝑒 𝐾𝑒 PERSON iajs-1821 69 2 ∈ ORG iajs-1821 69 3 6 CARDINAL iajs-1821 69 4 earlier DATE iajs-1821 69 5 eq.(3 ORG iajs-1821 69 6 π·βˆ— 𝑒 𝑃 𝐾𝑒 PERSON iajs-1821 69 7 ∈ ORG iajs-1821 71 1 un ORG iajs-1821 71 2 π‘βˆ— ORG iajs-1821 72 1 pgm ORG iajs-1821 73 1 2 CARDINAL iajs-1821 73 2 βŒ©π·βˆ— 𝑒 𝐾 𝑒 PERSON iajs-1821 73 3 π‘βˆ— ORG iajs-1821 73 4 π‘βˆ— ORG iajs-1821 73 5 1 CARDINAL iajs-1821 73 6 8) 4 DATE iajs-1821 73 7 pgm ORG iajs-1821 73 8 pgm ORG iajs-1821 73 9 six degree QUANTITY iajs-1821 73 10 0 CARDINAL iajs-1821 73 11 1 CARDINAL iajs-1821 73 12 ∈ ORG iajs-1821 75 1 1 CARDINAL iajs-1821 75 2 9 CARDINAL iajs-1821 75 3 10 CARDINAL iajs-1821 77 1 eq.(9),we GPE iajs-1821 77 2 11 CARDINAL iajs-1821 77 3 2017 CARDINAL iajs-1821 77 4 al-haitham ORG iajs-1821 77 5 10.30526/2017.ihsciconf.1821 CARDINAL iajs-1821 77 6 http://www.ihsciconf.org/conf/ PERSON iajs-1821 77 7 www.ihsciconf.org CARDINAL iajs-1821 78 1 12 CARDINAL iajs-1821 78 2 petrov-galerkin PERSON iajs-1821 78 3 pgm ORG iajs-1821 81 1 13 CARDINAL iajs-1821 83 1 βˆ— CARDINAL iajs-1821 85 1 14 CARDINAL iajs-1821 86 1 16 CARDINAL iajs-1821 87 1 𝐴 ORG iajs-1821 87 2 π‘Ž 5 DATE iajs-1821 87 3 1 CARDINAL iajs-1821 87 4 3π‘₯ MONEY iajs-1821 87 5 0 CARDINAL iajs-1821 87 6 0 CARDINAL iajs-1821 87 7 1 CARDINAL iajs-1821 88 1 2017 CARDINAL iajs-1821 88 2 al-haitham ORG iajs-1821 88 3 10.30526/2017.ihsciconf.1821 CARDINAL iajs-1821 88 4 http://www.ihsciconf.org/conf/ PERSON iajs-1821 88 5 www.ihsciconf.org CARDINAL iajs-1821 88 6 1 CARDINAL iajs-1821 89 1 1,0.5,0.25 CARDINAL iajs-1821 89 2 1 CARDINAL iajs-1821 89 3 0.5 CARDINAL iajs-1821 89 4 0.25 CARDINAL iajs-1821 89 5 0.064 CARDINAL iajs-1821 89 6 0.064 CARDINAL iajs-1821 89 7 1.6817 CARDINAL iajs-1821 89 8 3.072 MONEY iajs-1821 89 9 1 CARDINAL iajs-1821 89 10 2 CARDINAL iajs-1821 89 11 0 CARDINAL iajs-1821 89 12 1 CARDINAL iajs-1821 89 13 0.1 0.2 0.3 0.4 0.5 0.6 0.7 QUANTITY iajs-1821 89 14 0.5 1 1.5 2 QUANTITY iajs-1821 89 15 3 3.5 CARDINAL iajs-1821 89 16 1 CARDINAL iajs-1821 89 17 0.5 CARDINAL iajs-1821 89 18 0.25 CARDINAL iajs-1821 89 19 2017 CARDINAL iajs-1821 89 20 al-haitham ORG iajs-1821 89 21 10.30526/2017.ihsciconf.1821 CARDINAL iajs-1821 89 22 http://www.ihsciconf.org/conf/ PERSON iajs-1821 89 23 2 CARDINAL iajs-1821 89 24 1 CARDINAL iajs-1821 89 25 0.5 CARDINAL iajs-1821 89 26 0.25 CARDINAL iajs-1821 89 27 1.3953 CARDINAL iajs-1821 89 28 6.9920 MONEY iajs-1821 89 29 2 CARDINAL iajs-1821 89 30 3 CARDINAL iajs-1821 90 1 1 1 CARDINAL iajs-1821 90 2 0 CARDINAL iajs-1821 90 3 1 CARDINAL iajs-1821 90 4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 QUANTITY iajs-1821 90 5 0.9 1 CARDINAL iajs-1821 90 6 0 1 2 3 4 5 6 7 QUANTITY iajs-1821 90 7 1 CARDINAL iajs-1821 90 8 0.5 CARDINAL iajs-1821 90 9 0.25 CARDINAL iajs-1821 90 10 2017 CARDINAL iajs-1821 90 11 al-haitham ORG iajs-1821 90 12 10.30526/2017.ihsciconf.1821 CARDINAL iajs-1821 90 13 http://www.ihsciconf.org/conf/ PERSON iajs-1821 90 14 1,0.5,0.25 CARDINAL iajs-1821 90 15 1 CARDINAL iajs-1821 90 16 0.5 CARDINAL iajs-1821 90 17 0.25 CARDINAL iajs-1821 90 18 0.2 0.19867 CARDINAL iajs-1821 90 19 0.3 CARDINAL iajs-1821 90 20 0.4 CARDINAL iajs-1821 90 21 0.5 0.47943 CARDINAL iajs-1821 90 22 2.8152 CARDINAL iajs-1821 90 23 0.7 CARDINAL iajs-1821 90 24 3.6376 MONEY iajs-1821 90 25 0.8 CARDINAL iajs-1821 91 1 0.9 0.78333 0.77956 5.1083 QUANTITY iajs-1821 91 2 1 CARDINAL iajs-1821 91 3 6.2313 TIME iajs-1821 91 4 3 CARDINAL iajs-1821 91 5 6.conclusions CARDINAL iajs-1821 93 1 petrov-galerkin method(pgm PERSON iajs-1821 93 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 QUANTITY iajs-1821 93 3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 QUANTITY iajs-1821 93 4 1 CARDINAL iajs-1821 93 5 0.25 CARDINAL iajs-1821 93 6 0.5 CARDINAL iajs-1821 93 7 2017 CARDINAL iajs-1821 93 8 al-haitham ORG iajs-1821 93 9 10.30526/2017.ihsciconf.1821 CARDINAL iajs-1821 93 10 http://www.ihsciconf.org/conf/ PERSON iajs-1821 93 11 linear fractional volterra integro-differential ORG iajs-1821 93 12 second ORDINAL iajs-1821 94 1 linear ORG iajs-1821 94 2 second ORDINAL iajs-1821 94 3 1is ORDINAL iajs-1821 94 4 1 CARDINAL iajs-1821 94 5 2 CARDINAL iajs-1821 94 6 figure3 ORG iajs-1821 97 1 1 CARDINAL iajs-1821 97 2 z. taheri PERSON iajs-1821 97 3 336 CARDINAL iajs-1821 97 4 2017 CARDINAL iajs-1821 98 1 2 CARDINAL iajs-1821 98 2 jani PERSON iajs-1821 98 3 bhatta ORG iajs-1821 98 4 98 CARDINAL iajs-1821 98 5 2017 CARDINAL iajs-1821 99 1 3 CARDINAL iajs-1821 99 2 a. asma PERSON iajs-1821 99 3 k. adem PERSON iajs-1821 99 4 m. bachok PERSON iajs-1821 99 5 king saud university ORG iajs-1821 99 6 2016 DATE iajs-1821 100 1 4 CARDINAL iajs-1821 100 2 h. li PERSON iajs-1821 100 3 f. xian PERSON iajs-1821 100 4 z. yulin PERSON iajs-1821 100 5 y. xiang PERSON iajs-1821 100 6 taylor PERSON iajs-1821 100 7 applications,.1127-1134 WORK_OF_ART iajs-1821 101 1 2011 DATE iajs-1821 101 2 5 CARDINAL iajs-1821 101 3 l. peter PERSON iajs-1821 101 4 linear integro-differential ORG iajs-1821 101 5 siam journal ORG iajs-1821 101 6 144 CARDINAL iajs-1821 101 7 2006 DATE iajs-1821 102 1 6 CARDINAL iajs-1821 102 2 m. mayada PERSON iajs-1821 102 3 bernstein polynomial's ORG iajs-1821 102 4 baghdad GPE iajs-1821 102 5 journal,.1295-1300 ORG iajs-1821 102 6 2014 DATE iajs-1821 103 1 7 CARDINAL iajs-1821 103 2 m. khodabin PERSON iajs-1821 103 3 k. maleknejad PERSON iajs-1821 103 4 2014 DATE