Solutions of system of Volterra integro‐differential equations using optimal homotopy asymptotic method
In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra integro‐differential equations. The effectiveness and performance of the proposed technique are verified by different numerical problems in th...
Saved in:
| Published in | Mathematical methods in the applied sciences Vol. 44; no. 3; pp. 2671 - 2681 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Freiburg
Wiley Subscription Services, Inc
01.02.2021
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra integro‐differential equations. The effectiveness and performance of the proposed technique are verified by different numerical problems in the literature, and the obtained results are compared with Sinc‐collocation method. These results show the reliability and effectiveness of the proposed method. The proposed method does not require discretization like other numerical methods. Moreover, the convergence region can easily be controlled. The use of OHAM is simple and straightforward. |
|---|---|
| AbstractList | In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra integro‐differential equations. The effectiveness and performance of the proposed technique are verified by different numerical problems in the literature, and the obtained results are compared with Sinc‐collocation method. These results show the reliability and effectiveness of the proposed method. The proposed method does not require discretization like other numerical methods. Moreover, the convergence region can easily be controlled. The use of OHAM is simple and straightforward. |
| Author | Nawaz, Rashid Jleli, Mohamed Akbar, Muhammad Agarwal, Praveen |
| Author_xml | – sequence: 1 givenname: Praveen orcidid: 0000-0001-7556-8942 surname: Agarwal fullname: Agarwal, Praveen email: goyal.praveen2011@gmail.com organization: Institute of Mathematics and Mathematical Modeling – sequence: 2 givenname: Muhammad surname: Akbar fullname: Akbar, Muhammad organization: Abdul Wali Khan University Mardan – sequence: 3 givenname: Rashid orcidid: 0000-0002-4773-8446 surname: Nawaz fullname: Nawaz, Rashid organization: Abdul Wali Khan University Mardan – sequence: 4 givenname: Mohamed orcidid: 0000-0002-6095-5875 surname: Jleli fullname: Jleli, Mohamed organization: King Saud University |
| BookMark | eNp1kEtOwzAQQC1UJEpB4giR2LBJGdtpUi-rip_UigUVWyuJx62rJE5tRyg7jsAZOQkpZctqRjNvPnqXZNTYBgm5oTClAOy-rvNpms35GRlTECKmSZaOyBhoBnHCaHJBLr3fA8CcUjYm5s1WXTC28ZHVke99wPqYvdsqoHN5ZJqAW2e_P7-U0RodNsHkVYSHLj-Ndd4028i2wdRDfWdrG2zbR7nv6zbYYMqoxrCz6oqc67zyeP0XJ2Tz-LBZPser16eX5WIVl0xwHvMCkVOa8JSlZSGKolA8FYnQmS5SqgTVlAPkQ2uuQIBCNmPAhVBasQwpn5Db09rW2UOHPsi97VwzXJQsyWbAGROzgbo7UaWz3jvUsnXD_66XFOTRoxw8yqPHAY1P6IepsP-Xk-v14pf_AeTveQU |
| CitedBy_id | crossref_primary_10_1186_s13662_020_03087_w crossref_primary_10_3390_fractalfract5040159 crossref_primary_10_1007_s40819_022_01289_2 crossref_primary_10_1186_s13662_020_03077_y crossref_primary_10_52280_pujm_2021_530805 crossref_primary_10_1016_j_apnum_2021_06_013 crossref_primary_10_1109_ACCESS_2022_3141707 crossref_primary_10_37394_23206_2024_23_43 crossref_primary_10_1155_2021_5544540 crossref_primary_10_1002_mma_7128 crossref_primary_10_3390_math11061390 crossref_primary_10_1142_S0218348X22400163 crossref_primary_10_1155_2022_4791454 crossref_primary_10_3390_pr10061143 crossref_primary_10_1186_s13662_020_02990_6 crossref_primary_10_1155_2021_6690049 crossref_primary_10_37394_23206_2022_21_14 crossref_primary_10_1186_s13662_021_03449_y |
| Cites_doi | 10.1016/j.icheatmasstransfer.2008.02.010 10.1016/j.aej.2014.04.004 10.1155/2013/278097 10.3233/IFS-120732 10.12988/ijcms.2013.13052 10.22436/jmcs.05.04.02 10.1155/2014/725648 10.4236/am.2011.29152 10.11648/j.ijtam.20190506.14 10.5899/2013/cna-00186 |
| ContentType | Journal Article |
| Copyright | 2020 John Wiley & Sons, Ltd. 2021 John Wiley & Sons, Ltd. |
| Copyright_xml | – notice: 2020 John Wiley & Sons, Ltd. – notice: 2021 John Wiley & Sons, Ltd. |
| DBID | AAYXX CITATION 7TB 8FD FR3 JQ2 KR7 |
| DOI | 10.1002/mma.6783 |
| DatabaseName | CrossRef Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Engineering Research Database Technology Research Database Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection |
| DatabaseTitleList | CrossRef Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Sciences (General) Mathematics |
| EISSN | 1099-1476 |
| EndPage | 2681 |
| ExternalDocumentID | 10_1002_mma_6783 MMA6783 |
| Genre | article |
| GrantInformation_xml | – fundername: King Saud University funderid: RSP‐2020/57 |
| GroupedDBID | -~X .3N .GA .Y3 05W 0R~ 10A 1L6 1OB 1OC 1ZS 31~ 33P 3SF 3WU 4.4 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5GY 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHHS AANLZ AAONW AASGY AAXRX AAZKR ABCQN ABCUV ABIJN ABJNI ABPVW ACAHQ ACBWZ ACCFJ ACCZN ACGFS ACIWK ACPOU ACSCC ACXBN ACXQS ADBBV ADEOM ADIZJ ADKYN ADMGS ADOZA ADXAS ADZMN AEEZP AEIGN AEIMD AENEX AEQDE AEUQT AEUYR AFBPY AFFPM AFGKR AFPWT AFZJQ AHBTC AITYG AIURR AIWBW AJBDE AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN AMBMR AMYDB ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BY8 CO8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS EJD F00 F01 F04 F5P FEDTE G-S G.N GBZZK GNP GODZA H.T H.X HBH HF~ HGLYW HHY HVGLF HZ~ IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES M6O MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 NF~ O66 O9- OIG P2P P2W P2X P4D PALCI Q.N Q11 QB0 QRW R.K RIWAO RJQFR ROL RWI RWS RX1 RYL SAMSI SUPJJ UB1 V2E W8V W99 WBKPD WH7 WIB WIH WIK WOHZO WQJ WRC WXSBR WYISQ XBAML XG1 XPP XV2 ZZTAW ~02 ~IA ~WT AAYXX CITATION 7TB 8FD FR3 JQ2 KR7 |
| ID | FETCH-LOGICAL-c2933-3bee31143626cb9bbbd36949f7fb61d91f1300acb98d090de2520399dfd27e13 |
| IEDL.DBID | DR2 |
| ISSN | 0170-4214 |
| IngestDate | Thu Oct 10 16:49:49 EDT 2024 Fri Aug 23 03:46:37 EDT 2024 Sat Aug 24 01:13:33 EDT 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c2933-3bee31143626cb9bbbd36949f7fb61d91f1300acb98d090de2520399dfd27e13 |
| ORCID | 0000-0001-7556-8942 0000-0002-4773-8446 0000-0002-6095-5875 |
| PQID | 2475032295 |
| PQPubID | 1016386 |
| PageCount | 11 |
| ParticipantIDs | proquest_journals_2475032295 crossref_primary_10_1002_mma_6783 wiley_primary_10_1002_mma_6783_MMA6783 |
| PublicationCentury | 2000 |
| PublicationDate | February 2021 2021-02-00 20210201 |
| PublicationDateYYYYMMDD | 2021-02-01 |
| PublicationDate_xml | – month: 02 year: 2021 text: February 2021 |
| PublicationDecade | 2020 |
| PublicationPlace | Freiburg |
| PublicationPlace_xml | – name: Freiburg |
| PublicationTitle | Mathematical methods in the applied sciences |
| PublicationYear | 2021 |
| Publisher | Wiley Subscription Services, Inc |
| Publisher_xml | – name: Wiley Subscription Services, Inc |
| References | 2004; 155 2016; 6 2018; 5 2011; 2 2013; 2 2019; 5 2013; 2013 2007; 192 2008; 9 2014; 26 2017 2008; 35 2014; 2014 2013 2013; 8 2011; 5 2012; 5 2014; 53 Ghazanfari B (e_1_2_8_18_1) 2013; 2013 Berenguer MI (e_1_2_8_8_1) 2017 e_1_2_8_13_1 e_1_2_8_15_1 Matinfar M (e_1_2_8_3_1) 2014; 26 Maleknejad K (e_1_2_8_10_1) 2004; 155 Hashmia MS (e_1_2_8_17_1) 2016; 6 Hesameddini E (e_1_2_8_20_1) 2013; 2 Yusufoğlu E (e_1_2_8_2_1) 2007; 192 Akbar M (e_1_2_8_19_1) 2019; 5 Hesameddini ESMAIL (e_1_2_8_9_1) 2013; 2 Al‐Smadi M (e_1_2_8_6_1) 2013; 8 Rabbani M (e_1_2_8_12_1) 2012; 5 Davari A (e_1_2_8_11_1) 2011; 5 e_1_2_8_4_1 Almousa M (e_1_2_8_16_1) 2013 Herişanu N (e_1_2_8_14_1) 2008; 9 Loh JR (e_1_2_8_5_1) 2018; 5 Biazar J (e_1_2_8_7_1) 2011; 2 |
| References_xml | – volume: 26 start-page: 1095 issue: 3 year: 2014 end-page: 1102 article-title: Homotopy analysis method for systems of integro‐differential equations publication-title: Journal of Intelligent & Fuzzy Systems – volume: 53 start-page: 751 issue: 3 year: 2014 end-page: 755 article-title: Optimal homotopy asymptotic method for solving Volterra integral equation of first kind publication-title: Alex Eng J – volume: 6 start-page: 162 issue: 4S year: 2016 end-page: 166 article-title: Exact solution of Fredholmintegro‐differential equations using optimal homotopy asymptotic method publication-title: Journal of Applied Environmental and Biological Sciences – volume: 5 start-page: 2356 issue: 12 year: 2011 end-page: 2361 article-title: Solution of system of Fredholm integro differential equations by Adomian decomposition method publication-title: Australian Journal of Basic and Applied Sciences – volume: 2 start-page: 1105 issue: 9 year: 2011 end-page: 1113 article-title: A strong method for solving systems of integro‐differential equations publication-title: Applied Mathematics – volume: 2 start-page: 1 issue: 7 year: 2013 end-page: 9 article-title: Solving systems of linear Volterra integro‐differential equations by using Sinc‐collocation method publication-title: International Journal of Mathematical Engineering and Science – start-page: 1 year: 2017 end-page: 18 article-title: Solution of systems of integro‐differential equations using numerical treatment of fixed point publication-title: Journal of Computational and Applied Mathematics – start-page: 1 year: 2013 end-page: 6 article-title: Optimal homotopy asymptotic method for solving the linear Fredholm integral equations of the first kind publication-title: Abstract and Applied Analysis – volume: 2013 start-page: 1 year: 2013 end-page: 15 article-title: Optimal homotopy asymptotic method for solving system of Fredholm integral equations publication-title: Communications in Numerical Analysis – volume: 155 start-page: 317 issue: 2 year: 2004 end-page: 328 article-title: Solving linear integro‐differential equations system by using rationalized Haar functions method publication-title: Appl Math Comput – volume: 5 start-page: 1117 year: 2018 end-page: 1124 article-title: A new numerical scheme for solving system of Volterra integro‐differential equation publication-title: Alexandria Engineering Journal – volume: 5 start-page: 258 issue: 4 year: 2012 end-page: 264 article-title: Solution of Fredholm integro‐differential equations system by modified decomposition method publication-title: Journal of Mathematics and Computer Science – volume: 5 start-page: 100 issue: 6 year: 2019 end-page: 112 article-title: Optimum solutions of Fredholm and Volterra integro‐differential equations publication-title: International Journal of Theoretical and Applied Mathematics – volume: 8 start-page: 531 issue: 11 year: 2013 end-page: 540 article-title: Solution of system of Fredholm integro‐differential equations by RKHS method publication-title: International Journal of Contemporary Mathematical Sciences – volume: 2014 start-page: 1 year: 2014 end-page: 5 article-title: Solving systems of Volterra integral and integrodifferential equations with proportional delays by differential transformation method publication-title: Journal of Mathematics – volume: 9 start-page: 229 issue: 3 year: 2008 end-page: 236 article-title: A new analytical approach to nonlinear vibration of an electrical machine publication-title: Proceedings of the Romanian Academy‐Series A – volume: 35 start-page: 710 issue: 6 year: 2008 end-page: 715 article-title: Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer publication-title: International Communications in Heat and Mass Transfer – volume: 192 start-page: 51 issue: 1 year: 2007 end-page: 55 article-title: An efficient algorithm for solving integro‐differential equations system publication-title: Appl Math Comput – ident: e_1_2_8_13_1 doi: 10.1016/j.icheatmasstransfer.2008.02.010 – start-page: 1 year: 2017 ident: e_1_2_8_8_1 article-title: Solution of systems of integro‐differential equations using numerical treatment of fixed point publication-title: Journal of Computational and Applied Mathematics contributor: fullname: Berenguer MI – ident: e_1_2_8_15_1 doi: 10.1016/j.aej.2014.04.004 – start-page: 1 year: 2013 ident: e_1_2_8_16_1 article-title: Optimal homotopy asymptotic method for solving the linear Fredholm integral equations of the first kind publication-title: Abstract and Applied Analysis doi: 10.1155/2013/278097 contributor: fullname: Almousa M – volume: 9 start-page: 229 issue: 3 year: 2008 ident: e_1_2_8_14_1 article-title: A new analytical approach to nonlinear vibration of an electrical machine publication-title: Proceedings of the Romanian Academy‐Series A contributor: fullname: Herişanu N – volume: 155 start-page: 317 issue: 2 year: 2004 ident: e_1_2_8_10_1 article-title: Solving linear integro‐differential equations system by using rationalized Haar functions method publication-title: Appl Math Comput contributor: fullname: Maleknejad K – volume: 26 start-page: 1095 issue: 3 year: 2014 ident: e_1_2_8_3_1 article-title: Homotopy analysis method for systems of integro‐differential equations publication-title: Journal of Intelligent & Fuzzy Systems doi: 10.3233/IFS-120732 contributor: fullname: Matinfar M – volume: 8 start-page: 531 issue: 11 year: 2013 ident: e_1_2_8_6_1 article-title: Solution of system of Fredholm integro‐differential equations by RKHS method publication-title: International Journal of Contemporary Mathematical Sciences doi: 10.12988/ijcms.2013.13052 contributor: fullname: Al‐Smadi M – volume: 5 start-page: 258 issue: 4 year: 2012 ident: e_1_2_8_12_1 article-title: Solution of Fredholm integro‐differential equations system by modified decomposition method publication-title: Journal of Mathematics and Computer Science doi: 10.22436/jmcs.05.04.02 contributor: fullname: Rabbani M – ident: e_1_2_8_4_1 doi: 10.1155/2014/725648 – volume: 2 start-page: 1105 issue: 9 year: 2011 ident: e_1_2_8_7_1 article-title: A strong method for solving systems of integro‐differential equations publication-title: Applied Mathematics doi: 10.4236/am.2011.29152 contributor: fullname: Biazar J – volume: 6 start-page: 162 issue: 4 year: 2016 ident: e_1_2_8_17_1 article-title: Exact solution of Fredholmintegro‐differential equations using optimal homotopy asymptotic method publication-title: Journal of Applied Environmental and Biological Sciences contributor: fullname: Hashmia MS – volume: 5 start-page: 1117 year: 2018 ident: e_1_2_8_5_1 article-title: A new numerical scheme for solving system of Volterra integro‐differential equation publication-title: Alexandria Engineering Journal contributor: fullname: Loh JR – volume: 5 start-page: 100 issue: 6 year: 2019 ident: e_1_2_8_19_1 article-title: Optimum solutions of Fredholm and Volterra integro‐differential equations publication-title: International Journal of Theoretical and Applied Mathematics doi: 10.11648/j.ijtam.20190506.14 contributor: fullname: Akbar M – volume: 192 start-page: 51 issue: 1 year: 2007 ident: e_1_2_8_2_1 article-title: An efficient algorithm for solving integro‐differential equations system publication-title: Appl Math Comput contributor: fullname: Yusufoğlu E – volume: 2 start-page: 1 issue: 7 year: 2013 ident: e_1_2_8_9_1 article-title: Solving systems of linear Volterra integro‐differential equations by using Sinc‐collocation method publication-title: International Journal of Mathematical Engineering and Science contributor: fullname: Hesameddini ESMAIL – volume: 2 start-page: 1 issue: 7 year: 2013 ident: e_1_2_8_20_1 article-title: Solving systems of linear Volterra integro‐differential equations by using Sinc‐collocation method publication-title: International Journal of Mathematical Engineering and Science contributor: fullname: Hesameddini E – volume: 5 start-page: 2356 issue: 12 year: 2011 ident: e_1_2_8_11_1 article-title: Solution of system of Fredholm integro differential equations by Adomian decomposition method publication-title: Australian Journal of Basic and Applied Sciences contributor: fullname: Davari A – volume: 2013 start-page: 1 year: 2013 ident: e_1_2_8_18_1 article-title: Optimal homotopy asymptotic method for solving system of Fredholm integral equations publication-title: Communications in Numerical Analysis doi: 10.5899/2013/cna-00186 contributor: fullname: Ghazanfari B |
| SSID | ssj0008112 |
| Score | 2.4004488 |
| Snippet | In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra... |
| SourceID | proquest crossref wiley |
| SourceType | Aggregation Database Publisher |
| StartPage | 2671 |
| SubjectTerms | approximate solutions Asymptotic methods Collocation methods Differential equations Numerical methods optimal homotopy asymptotic method system of Volterra integro‐differential equations Volterra integral equations |
| Title | Solutions of system of Volterra integro‐differential equations using optimal homotopy asymptotic method |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fmma.6783 https://www.proquest.com/docview/2475032295 |
| Volume | 44 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ3PT4MwFMcbs5Me1E2N02lqYowe2KAUWI-LcVlM8GCmWeKBUFrUKGMOdpgn_wT_Rv8S-yhsamJi5ALhR4C27_GF9_g8hI4ZcR01MSP2HGkoL6lMCrCVhEkaSZvHjoCIrn_lDm7o5cgZlVmV8C-M5kMsPriBZRT-Ggw85FlnCQ1NkrCtPC2APoGjB3roekmO6lpFoBPoMAYlFq24sybpVAd-fxIt5eVXkVo8Zfob6K66Pp1c8tSe5bwdvf5AN_7vBjbReik-cU-PljpakeMGWvMX5NasgeqlsWf4tCRSn22hx8XHM5zGWMOfYek2hVj7NMQaOpF-vL1XBVeU43jG8kWDxDMM6fX3OFX-KVHrHyAFMJ3McZjNk0meqlNjXcp6Gw37F8PzgVHWaDAiJRRsw-ZS2uqdCqg2EWecc2G7jLLYi7lrCWbFEC8L1aauMJkpJHGIqUSRiAXxpGXvoNo4HctdhD1qCpOGSg85gkpJGY9dRzoyCm2ohG030VHVXcFEkzgCzVwmgWrKAJqyiVpVPwalLWYBoRCrhbLlTXRSdMivxwe-34P53l933EerBJJcijTuFqrl05k8UCol54fFePwEIojmLg |
| link.rule.ids | 315,786,790,1382,27955,27956,46327,46751 |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ1LT9wwEIBHPA7QA6-2YnkaCSF6yG7iRxaLE-KhpSUc0FJxqBTFsVOqdjcLWQ5w4ifwG_kleOJkFypVqsglURLLie0ZTzyTbwC2JQ2F3aSXtYXxrJa0IoXYSioNTw1TmdDo0Y3Ow84l_3olriZgv_4XxvEhRgtuKBmlvkYBxwXp1pga2uslTatq2SRMW2kXKJVHF2N21F5QujqRD-NxGvCaPOvTVl3y7Vw0NjBfm6nlPHMyDz_qJ3ThJb-bd0PVTB_-gje-8xUWYK6yP8mBGzCLMGH6S_AhGsFbiyVYrOS9ILsVlPrLR_g1Wj8jeUYc_xmPvufobr9NiONO5M-PT3XOFas7_hBz41jiBcEI-58ktyqqZ89fYxRgPrgnSXHfGwxzWzVx2aw_QffkuHvY8ao0DV5qbQXmMWUMs59VCLZJlVRKaRZKLrN2psJAyyBDl1liL-1pX_raUEF9axfpTNO2CdhnmOrnfbMMpM197fPEmkRCc2O4VFkojDBpwjAZNmvAVt1f8cDBOGKHXaaxbcoYm7IBa3VHxpU4FjHl6K7FzOUN2Cl75J_l4yg6wP3K_964CTOdbnQWn52ef1uFWYoxL2VU9xpMDW_vzLo1WoZqoxycL4fS6k4 |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ3dS-QwEMAHP0D0wW9x_bocHKIPXdsk7ZpHURc9XRFREXwoTZOo6G5Xuz7o0_0J9zf6l5hp2l1PEOT60tI2tE0yk0lm-huAX4JGod2EZxqh9qyWtCKF2EoqNE81kyZU6NFtnUQHF_z3VXhVRlXivzCOD9FfcEPJKPQ1CnhXma0BNLTdTupW07JhGOURozjx2jsboKO2g8LTiXgYj9OAV-BZn25VJf8digb25UcrtRhmmlNwXb2giy65rz_3ZD19_cRu_L8vmIbJ0vokO667zMCQ7szCRKuPbs1nYaaU9pxslEjqzTm466-ekcwQR3_Go8sMne1PCXHUieztz98q44rVHA9EPzqSeE4wvv6GZFZBte35W4wBzLovJMlf2t1eZh9NXC7reThv7p_vHnhlkgYvtZYC85jUmtlJFWJtUimklIpFggvTMDIKlAgMOswSe2lb-cJXmobUt1aRMoo2dMAWYKSTdfQikAb3lc8TaxCFimvNhTRRqEOdJgxTYbMa_KyaK-46FEfsoMs0tlUZY1XWYKVqx7gUxjymHJ21mLe8ButFg3xZPm61dnC_9N0bf8DY6V4zPj48OVqGcYoBL0VI9wqM9J6e9aq1WHpyreia7-oh6P0 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Solutions+of+system+of+Volterra+integro%E2%80%90differential+equations+using+optimal+homotopy+asymptotic+method&rft.jtitle=Mathematical+methods+in+the+applied+sciences&rft.au=Agarwal%2C+Praveen&rft.au=Akbar%2C+Muhammad&rft.au=Nawaz%2C+Rashid&rft.au=Jleli%2C+Mohamed&rft.date=2021-02-01&rft.issn=0170-4214&rft.eissn=1099-1476&rft.volume=44&rft.issue=3&rft.spage=2671&rft.epage=2681&rft_id=info:doi/10.1002%2Fmma.6783&rft.externalDBID=10.1002%252Fmma.6783&rft.externalDocID=MMA6783 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0170-4214&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0170-4214&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0170-4214&client=summon |