Numerical algorithm for solving time‐fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions
Recently, many new applications in engineering and science are governed by a series of time‐fractional partial integrodifferential equations, which will lead to new challenges for numerical simulation. In this article, we propose and analyze an efficient iterative algorithm for the numerical solutio...
Saved in:
| Published in | Numerical methods for partial differential equations Vol. 34; no. 5; pp. 1577 - 1597 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Wiley Subscription Services, Inc
01.09.2018
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0749-159X 1098-2426 1098-2426 |
| DOI | 10.1002/num.22209 |
Cover
| Abstract | Recently, many new applications in engineering and science are governed by a series of time‐fractional partial integrodifferential equations, which will lead to new challenges for numerical simulation. In this article, we propose and analyze an efficient iterative algorithm for the numerical solutions of such equations subject to initial and Dirichlet boundary conditions. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the
n
‐term of exact solutions, numerical solutions of linear and nonlinear time‐fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds under some hypotheses which provide the theoretical basis of the proposed algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such integrodifferential equations. |
|---|---|
| AbstractList | Recently, many new applications in engineering and science are governed by a series of time‐fractional partial integrodifferential equations, which will lead to new challenges for numerical simulation. In this article, we propose and analyze an efficient iterative algorithm for the numerical solutions of such equations subject to initial and Dirichlet boundary conditions. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n‐term of exact solutions, numerical solutions of linear and nonlinear time‐fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds under some hypotheses which provide the theoretical basis of the proposed algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such integrodifferential equations. Recently, many new applications in engineering and science are governed by a series of time‐fractional partial integrodifferential equations, which will lead to new challenges for numerical simulation. In this article, we propose and analyze an efficient iterative algorithm for the numerical solutions of such equations subject to initial and Dirichlet boundary conditions. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the ‐term of exact solutions, numerical solutions of linear and nonlinear time‐fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds under some hypotheses which provide the theoretical basis of the proposed algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such integrodifferential equations. Recently, many new applications in engineering and science are governed by a series of time‐fractional partial integrodifferential equations, which will lead to new challenges for numerical simulation. In this article, we propose and analyze an efficient iterative algorithm for the numerical solutions of such equations subject to initial and Dirichlet boundary conditions. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n ‐term of exact solutions, numerical solutions of linear and nonlinear time‐fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds under some hypotheses which provide the theoretical basis of the proposed algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such integrodifferential equations. |
| Author | Al‐Smadi, Mohammed Abu Arqub, Omar |
| Author_xml | – sequence: 1 givenname: Omar orcidid: 0000-0001-9526-6095 surname: Abu Arqub fullname: Abu Arqub, Omar email: o.abuarqub@bau.edu.jo organization: Al‐Balqa Applied University – sequence: 2 givenname: Mohammed surname: Al‐Smadi fullname: Al‐Smadi, Mohammed organization: Ajloun College, Al‐Balqa Applied University |
| BookMark | eNp9kMtKAzEUhoMoWC8L3yDgSmFskrkvxTtU3Si4G9LMSU3JJDXJWLrzAVz4jD6JcepK0NWBnO__T_h20KaxBhA6oOSEEsLGpu9OGGOk3kAjSuoqYRkrNtGIlFmd0Lx-2kY73s8JoTSn9Qi93_UdOCW4xlzPrFPhucPSOuytflVmhoPq4PPtQzougrImcgvugopTmQAzZ1slJTgwwxu89Pwb89j30zmIgIONoBqW3LT4XMVjzxoCntretNytsLCmVUNoD21Jrj3s_8xd9Hh58XB2nUzur27OTieJSFNWJ7LgosoFUEYBZFvmIiuELKfFtMq4YHnZyiggyykRLQhOKpLXRZFRKGWWSpGlu-h43dubBV8tudbNwqkufqahpPn22ESPzeAxwodreOHsSw8-NHPbuyjCN4yUFatJXqaROlpTwlnvHch_G8e_WKHCoC04rvR_iaXSsPq7url7vF0nvgBQE6aj |
| CitedBy_id | crossref_primary_10_1007_s12190_018_1176_x crossref_primary_10_1016_j_chaos_2018_10_013 crossref_primary_10_1016_j_physa_2019_122149 crossref_primary_10_26117_2079_6641_2022_38_1_131_146 crossref_primary_10_3390_math8111972 crossref_primary_10_1007_s40314_019_0979_1 crossref_primary_10_3390_sym11020205 crossref_primary_10_1007_s11277_020_07085_9 crossref_primary_10_1002_fld_4901 crossref_primary_10_1007_s40314_019_0953_y crossref_primary_10_1016_j_cjph_2020_08_017 crossref_primary_10_1016_j_apnum_2020_12_007 crossref_primary_10_1080_00207160_2023_2214254 crossref_primary_10_1016_j_rinp_2021_104210 crossref_primary_10_1080_16583655_2019_1618547 crossref_primary_10_1007_s11071_019_04800_5 crossref_primary_10_1016_j_joes_2019_11_005 crossref_primary_10_1155_2018_8686502 crossref_primary_10_1002_num_22587 crossref_primary_10_1016_j_jnt_2021_12_013 crossref_primary_10_1016_j_chaos_2019_03_020 crossref_primary_10_1007_s12190_019_01241_6 crossref_primary_10_1108_HFF_11_2018_0700 crossref_primary_10_1016_j_chaos_2021_111127 crossref_primary_10_1142_S0217984921504923 crossref_primary_10_1142_S0218348X23401898 crossref_primary_10_1007_s12190_020_01353_4 crossref_primary_10_1186_s13662_019_2021_8 crossref_primary_10_1007_s11071_018_4459_8 crossref_primary_10_1088_1402_4896_abb420 crossref_primary_10_33187_jmsm_1595276 crossref_primary_10_1007_s11071_019_04921_x crossref_primary_10_1088_1402_4896_ac0867 crossref_primary_10_3390_app10030890 crossref_primary_10_1002_mma_5497 crossref_primary_10_1002_mma_5530 crossref_primary_10_1007_s10092_018_0274_3 crossref_primary_10_1016_j_chaos_2019_05_025 crossref_primary_10_1080_00207160_2018_1544367 crossref_primary_10_1007_s10473_020_0310_7 crossref_primary_10_1016_j_joes_2021_09_005 crossref_primary_10_1186_s13662_019_2042_3 crossref_primary_10_1002_mma_5812 crossref_primary_10_1007_s40314_019_0941_2 crossref_primary_10_1088_1572_9494_ab8a29 crossref_primary_10_1016_j_chaos_2019_109478 crossref_primary_10_1016_j_physa_2019_122271 crossref_primary_10_1002_num_22236 crossref_primary_10_1016_j_chaos_2019_109552 crossref_primary_10_1007_s00366_019_00807_z crossref_primary_10_1016_j_physa_2019_123257 crossref_primary_10_1016_j_physa_2019_121275 crossref_primary_10_3390_app9235029 crossref_primary_10_3390_fractalfract4020027 crossref_primary_10_1088_1402_4896_ab96e0 crossref_primary_10_1016_j_padiff_2021_100164 crossref_primary_10_1016_j_chaos_2019_06_014 crossref_primary_10_3390_fractalfract3010010 crossref_primary_10_1002_mma_9005 crossref_primary_10_1002_mma_7228 crossref_primary_10_1002_mma_7305 crossref_primary_10_1016_j_chaos_2019_06_009 crossref_primary_10_1007_s13398_019_00694_5 crossref_primary_10_1186_s13662_019_1996_5 crossref_primary_10_1016_j_chaos_2019_07_023 crossref_primary_10_1016_j_physa_2019_123494 crossref_primary_10_1007_s00366_022_01749_9 crossref_primary_10_1016_j_cam_2024_115867 crossref_primary_10_1016_j_physa_2019_122496 crossref_primary_10_1080_00207160_2022_2149264 crossref_primary_10_1016_j_enganabound_2024_02_015 crossref_primary_10_1016_j_matcom_2019_06_005 crossref_primary_10_1016_j_apnum_2019_04_014 crossref_primary_10_1016_j_amc_2018_09_020 crossref_primary_10_1016_j_aej_2021_12_044 crossref_primary_10_1002_mma_8079 crossref_primary_10_1016_j_aej_2020_03_003 crossref_primary_10_1108_HFF_10_2017_0394 crossref_primary_10_1007_s00500_020_04687_0 crossref_primary_10_1007_s00500_020_05313_9 crossref_primary_10_3390_math8060923 crossref_primary_10_1007_s40314_022_01790_w crossref_primary_10_1016_j_aej_2020_02_010 crossref_primary_10_1016_j_amc_2019_124727 crossref_primary_10_1016_j_apnum_2021_09_005 |
| Cites_doi | 10.1016/j.amc.2013.03.123 10.1007/s00521-015-2110-x 10.1016/j.aml.2011.10.025 10.1186/s13662-017-1085-6 10.1002/mma.3884 10.3233/FI-2016-1384 10.1016/j.cam.2013.04.040 10.1002/num.22153 10.1016/j.aml.2005.10.010 10.1007/s00500-015-1707-4 10.1016/j.camwa.2011.03.037 10.1007/s00521-016-2484-4 10.1016/j.amc.2013.03.006 10.1002/num.21809 10.1090/S0002-9947-1950-0051437-7 10.1016/j.aml.2013.05.006 10.1016/j.camwa.2006.02.011 10.1155/2014/162896 10.1007/s00009-017-0904-z 10.1155/2014/431965 10.1016/j.amc.2014.12.121 10.1016/S0165-1684(03)00181-6 10.1016/j.amc.2014.04.057 10.1016/j.jcp.2014.09.034 10.1016/j.apm.2015.01.021 10.1016/j.amc.2014.06.063 10.1007/s00500-016-2262-3 10.1016/j.camwa.2016.01.001 10.1016/S0304-0208(06)80001-0 10.1142/p614 10.1007/978-1-4419-9096-9 10.1007/s00521-017-2845-7 10.1016/j.cam.2009.01.012 10.1016/j.jcp.2014.08.004 10.1108/HFF-07-2016-0278 10.1016/j.camwa.2016.11.032 |
| ContentType | Journal Article |
| Copyright | 2017 Wiley Periodicals, Inc. 2018 Wiley Periodicals, Inc. |
| Copyright_xml | – notice: 2017 Wiley Periodicals, Inc. – notice: 2018 Wiley Periodicals, Inc. |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 H8D JQ2 KR7 L7M L~C L~D ADTOC UNPAY |
| DOI | 10.1002/num.22209 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database Aerospace Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Unpaywall for CDI: Periodical Content Unpaywall |
| DatabaseTitle | CrossRef Aerospace Database Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Aerospace Database CrossRef |
| Database_xml | – sequence: 1 dbid: UNPAY name: Unpaywall url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/ sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1098-2426 |
| EndPage | 1597 |
| ExternalDocumentID | 10.1002/num.22209 10_1002_num_22209 NUM22209 |
| Genre | article |
| GroupedDBID | -~X .3N .GA .Y3 05W 0R~ 10A 123 1L6 1OB 1OC 1ZS 31~ 33P 3SF 3WU 4.4 41~ 4ZD 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHHS AAHQN AAMNL AANHP AANLZ AAONW AASGY AAXRX AAYCA AAZKR ABCQN ABCUV ABDBF ABEML ABIJN ABJNI ACAHQ ACBWZ ACCFJ ACCZN ACGFS ACIWK ACPOU ACRPL ACSCC ACUHS ACXBN ACXQS ACYXJ ADBBV ADEOM ADIZJ ADKYN ADMGS ADNMO ADOZA ADXAS ADZMN AEEZP AEIGN AEIMD AENEX AEQDE AEUQT AEUYR AFBPY AFFNX AFFPM AFGKR AFPWT AFWVQ AFZJQ AHBTC AITYG AIURR AIWBW AJBDE AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMYDB ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BY8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM EBS EJD F00 F01 F04 F5P FEDTE G-S G.N GBZZK GNP GODZA H.T H.X HBH HF~ HGLYW HHY HVGLF HZ~ H~9 I-F 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 N9A NF~ NNB O66 O9- OIG P2P P2W P2X P4D PALCI PQQKQ Q.N Q11 QB0 QRW R.K RIWAO RJQFR ROL RWI RWS RX1 RYL SAMSI SUPJJ TN5 UB1 V2E W8V W99 WBKPD WH7 WIB WIH WIK WOHZO WQJ WRC WXSBR WYISQ XBAML XG1 XPP XV2 ZZTAW ~IA ~WT AAMMB AAYXX AEFGJ AEYWJ AGHNM AGQPQ AGXDD AGYGG AIDQK AIDYY AIQQE AMVHM CITATION 7SC 7TB 8FD FR3 H8D JQ2 KR7 L7M L~C L~D ADTOC UNPAY |
| ID | FETCH-LOGICAL-c3329-f6ac85ce121eefd75c46cf7b6b84ac257df2094510cdeca080596641e7f43fc43 |
| IEDL.DBID | UNPAY |
| ISSN | 0749-159X 1098-2426 |
| IngestDate | Wed Oct 01 16:28:46 EDT 2025 Fri Jul 25 12:27:00 EDT 2025 Wed Oct 01 04:09:15 EDT 2025 Thu Apr 24 22:57:00 EDT 2025 Wed Jan 22 16:47:49 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Language | English |
| License | http://onlinelibrary.wiley.com/termsAndConditions#vor |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c3329-f6ac85ce121eefd75c46cf7b6b84ac257df2094510cdeca080596641e7f43fc43 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-9526-6095 |
| OpenAccessLink | https://proxy.k.utb.cz/login?url=https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/num.22209 |
| PQID | 2078290573 |
| PQPubID | 1016406 |
| PageCount | 21 |
| ParticipantIDs | unpaywall_primary_10_1002_num_22209 proquest_journals_2078290573 crossref_primary_10_1002_num_22209 crossref_citationtrail_10_1002_num_22209 wiley_primary_10_1002_num_22209_NUM22209 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | September 2018 2018-09-00 20180901 |
| PublicationDateYYYYMMDD | 2018-09-01 |
| PublicationDate_xml | – month: 09 year: 2018 text: September 2018 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Numerical methods for partial differential equations |
| PublicationYear | 2018 |
| Publisher | Wiley Subscription Services, Inc |
| Publisher_xml | – name: Wiley Subscription Services, Inc |
| References | 2006; 52 2013; 26 2015; 39 1950; 68 2017; 2017 2010 2011; 62 2009 2016; 146 2006 2006; 19 2005 1993 2014; 2014 2016; 71 2004 2003 2009; 230 2016; 39 2008; 2008 2014; 255 1999 2017; 73 2015; 293 2013; 219 2017; 14 2015; 257 2017; 33 2016; 20 2017 2016 1982 2014; 30 2012; 25 2003; 83 2014; 243 2014; 240 1907; 39 e_1_2_10_46_1 e_1_2_10_24_1 e_1_2_10_45_1 Daniel A. (e_1_2_10_23_1) 2003 e_1_2_10_44_1 e_1_2_10_22_1 e_1_2_10_43_1 e_1_2_10_42_1 Samko S. G. (e_1_2_10_5_1) 1993 e_1_2_10_20_1 e_1_2_10_41_1 Podlubny I. (e_1_2_10_4_1) 1999 Zaslavsky G. M. (e_1_2_10_3_1) 2005 e_1_2_10_2_1 e_1_2_10_18_1 e_1_2_10_6_1 e_1_2_10_16_1 e_1_2_10_39_1 e_1_2_10_17_1 e_1_2_10_38_1 e_1_2_10_8_1 e_1_2_10_14_1 e_1_2_10_37_1 e_1_2_10_7_1 e_1_2_10_15_1 e_1_2_10_36_1 e_1_2_10_12_1 e_1_2_10_35_1 e_1_2_10_9_1 e_1_2_10_13_1 e_1_2_10_34_1 e_1_2_10_10_1 e_1_2_10_33_1 e_1_2_10_11_1 e_1_2_10_32_1 e_1_2_10_31_1 e_1_2_10_30_1 Yang L. H. (e_1_2_10_27_1) 2008; 2008 Abu Arqub O. (e_1_2_10_40_1) 2017 e_1_2_10_29_1 Cui M. (e_1_2_10_21_1) 2009 Zaremba S. (e_1_2_10_19_1) 1907; 39 e_1_2_10_28_1 e_1_2_10_25_1 e_1_2_10_26_1 |
| References_xml | – volume: 293 start-page: 385 year: 2015 end-page: 399 publication-title: J. Comput. Phys. – volume: 71 start-page: 859 year: 2016 end-page: 868 publication-title: Comput. Math. Appl. – year: 2009 – volume: 83 start-page: 2285 year: 2003 end-page: 2286 publication-title: Signal Process. – volume: 39 start-page: 147 year: 1907 end-page: 196 publication-title: Bull. Int. Acad. Sci. Cracov. – year: 2017 publication-title: J. Porous Media – year: 2005 – volume: 2008 start-page: 1 year: 2008 end-page: 11 publication-title: Electron. J. Differ. Equ. – volume: 73 start-page: 1243 year: 2017 end-page: 1261 publication-title: Comput. Math. Appl. – volume: 2014 start-page: 5 year: 2014 publication-title: Math. Probl. Eng. – year: 2003 – start-page: 1 year: 2016 end-page: 16 publication-title: Soft Comput. – volume: 243 start-page: 911 year: 2014 end-page: 922 publication-title: Appl. Math. Comput. – start-page: 1 year: 2017 end-page: 12 publication-title: Neural Comput. Appl. – volume: 39 start-page: 5592 year: 2015 end-page: 5597 publication-title: Appl. Math. Model. – volume: 293 start-page: 81 year: 2015 end-page: 95 publication-title: J. Comput. Phys. – volume: 20 start-page: 3283 year: 2016 end-page: 3302 publication-title: Soft Comput. – volume: 146 start-page: 231 year: 2016 end-page: 254 publication-title: Fundam. Inform. – start-page: 1591 year: 2017 end-page: 1610 publication-title: Neural Comput. Appl. – start-page: 1 year: 2016 end-page: 15 publication-title: Neural Comput. Appl. – year: 2010 – volume: 2014 start-page: 7 year: 2014 publication-title: Abstr. Appl. Anal. – volume: 2017 start-page: 27 year: 2017 publication-title: Adv. Differ. Equ. – volume: 25 start-page: 818 year: 2012 end-page: 823 publication-title: Appl. Math. Lett. – volume: 39 start-page: 4549 year: 2016 end-page: 4562 publication-title: Math. Methods Appl. Sci. – volume: 62 start-page: 1127 year: 2011 end-page: 1134 publication-title: Comput. Math. Appl. – volume: 33 year: 2017 publication-title: Numer. Methods Partial Differ. Equ. – year: 1982 – volume: 230 start-page: 770 year: 2009 end-page: 780 publication-title: J. Comput. Appl. Math. – volume: 68 start-page: 337 year: 1950 end-page: 404 publication-title: Trans. Am. Math. Soc. – volume: 219 start-page: 8938 year: 2013 end-page: 8948 publication-title: Appl. Math. Comput. – year: 2017 publication-title: Int. J. Numer. Methods Heat Fluid Flow – volume: 30 start-page: 289 year: 2014 end-page: 300 publication-title: Numer. Methods Partial Differ. Equ. – volume: 240 start-page: 229 year: 2014 end-page: 239 publication-title: Appl. Math. Comput. – year: 2006 – volume: 52 start-page: 459 year: 2006 end-page: 470 publication-title: Comput. Math. Appl. – year: 2004 – volume: 255 start-page: 97 year: 2014 end-page: 105 publication-title: J. Comput. Appl. Math. – volume: 257 start-page: 119 year: 2015 end-page: 133 publication-title: Appl. Math. Comput. – volume: 26 start-page: 998 year: 2013 end-page: 1004 publication-title: Appl. Math. Lett. – volume: 219 start-page: 10225 year: 2013 end-page: 10230 publication-title: Appl.00 Math. Comput. – volume: 19 start-page: 808 year: 2006 end-page: 813 publication-title: Appl. Math. Lett. – volume: 14 start-page: 113 year: 2017 publication-title: Mediterr. J. Math. – year: 1993 – year: 1999 – volume-title: Fractional differential equations year: 1999 ident: e_1_2_10_4_1 – volume-title: Fractional integrals and derivatives theory and applications year: 1993 ident: e_1_2_10_5_1 – ident: e_1_2_10_45_1 doi: 10.1016/j.amc.2013.03.123 – ident: e_1_2_10_36_1 doi: 10.1007/s00521-015-2110-x – ident: e_1_2_10_44_1 doi: 10.1016/j.aml.2011.10.025 – ident: e_1_2_10_13_1 doi: 10.1186/s13662-017-1085-6 – ident: e_1_2_10_30_1 doi: 10.1002/mma.3884 – ident: e_1_2_10_37_1 doi: 10.3233/FI-2016-1384 – ident: e_1_2_10_43_1 doi: 10.1016/j.cam.2013.04.040 – ident: e_1_2_10_7_1 doi: 10.1002/num.22153 – ident: e_1_2_10_25_1 doi: 10.1016/j.aml.2005.10.010 – ident: e_1_2_10_34_1 doi: 10.1007/s00500-015-1707-4 – ident: e_1_2_10_9_1 doi: 10.1016/j.camwa.2011.03.037 – ident: e_1_2_10_38_1 doi: 10.1007/s00521-016-2484-4 – ident: e_1_2_10_31_1 doi: 10.1016/j.amc.2013.03.006 – volume-title: Hamiltonian chaos and fractional dynamics year: 2005 ident: e_1_2_10_3_1 – ident: e_1_2_10_42_1 doi: 10.1002/num.21809 – ident: e_1_2_10_20_1 doi: 10.1090/S0002-9947-1950-0051437-7 – ident: e_1_2_10_41_1 doi: 10.1016/j.aml.2013.05.006 – ident: e_1_2_10_11_1 doi: 10.1016/j.camwa.2006.02.011 – ident: e_1_2_10_12_1 doi: 10.1155/2014/162896 – ident: e_1_2_10_24_1 – ident: e_1_2_10_8_1 doi: 10.1007/s00009-017-0904-z – volume-title: Reproducing kernel spaces and applications year: 2003 ident: e_1_2_10_23_1 – ident: e_1_2_10_10_1 doi: 10.1155/2014/431965 – volume: 39 start-page: 147 year: 1907 ident: e_1_2_10_19_1 article-title: L'equation biharminique et une class remarquable defonctionsfoundamentals harmoniques publication-title: Bull. Int. Acad. Sci. Cracov. – ident: e_1_2_10_15_1 doi: 10.1016/j.amc.2014.12.121 – ident: e_1_2_10_18_1 doi: 10.1016/S0165-1684(03)00181-6 – volume-title: Nonlinear numerical analysis in the reproducing kernel space year: 2009 ident: e_1_2_10_21_1 – ident: e_1_2_10_33_1 doi: 10.1016/j.amc.2014.04.057 – ident: e_1_2_10_14_1 doi: 10.1016/j.jcp.2014.09.034 – ident: e_1_2_10_46_1 doi: 10.1016/j.apm.2015.01.021 – ident: e_1_2_10_32_1 doi: 10.1016/j.amc.2014.06.063 – ident: e_1_2_10_35_1 doi: 10.1007/s00500-016-2262-3 – ident: e_1_2_10_17_1 doi: 10.1016/j.camwa.2016.01.001 – ident: e_1_2_10_6_1 doi: 10.1016/S0304-0208(06)80001-0 – volume: 2008 start-page: 1 year: 2008 ident: e_1_2_10_27_1 article-title: Reproducing kernel methods for solving linear initial‐boundary‐value problems publication-title: Electron. J. Differ. Equ. – ident: e_1_2_10_2_1 doi: 10.1142/p614 – ident: e_1_2_10_22_1 doi: 10.1007/978-1-4419-9096-9 – ident: e_1_2_10_29_1 doi: 10.1007/s00521-017-2845-7 – ident: e_1_2_10_26_1 doi: 10.1016/j.cam.2009.01.012 – year: 2017 ident: e_1_2_10_40_1 article-title: Application of reproducing kernel algorithm for solving Dirichlet time‐fractional diffusion‐Gordon types equations in porous media publication-title: J. Porous Media – ident: e_1_2_10_16_1 doi: 10.1016/j.jcp.2014.08.004 – ident: e_1_2_10_39_1 doi: 10.1108/HFF-07-2016-0278 – ident: e_1_2_10_28_1 doi: 10.1016/j.camwa.2016.11.032 |
| SSID | ssj0011519 |
| Score | 2.5148432 |
| Snippet | Recently, many new applications in engineering and science are governed by a series of time‐fractional partial integrodifferential equations, which will lead... |
| SourceID | unpaywall proquest crossref wiley |
| SourceType | Open Access Repository Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1577 |
| SubjectTerms | Algorithms Boundary conditions Computer simulation Dirichlet problem Error analysis fractional calculus theory Infinite series Iterative algorithms Iterative methods Nonlinear equations Numerical analysis partial integrodifferential equation reproducing kernel algorithm Simulated annealing |
| SummonAdditionalLinks | – databaseName: Wiley Online Library - Core collection (SURFmarket) dbid: DR2 link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9tAEF4hLpQDpQVECkWrwoGLA16_1uJUVSBUKTkgIuWAZO0TIhwnxLYQnPgBHPiN_JLO7sZuQS2qONmyx5bXnsc3491vENpjgYo4SYinfJ6Y0g3xmNTSS3yfEyoTHtleh71-fDoIfw6j4QI6atbCOH6ItuBmLMP6a2PgjJcHf5CG1uMuBDe7eM8PYptOnbXUUQB0bFMPiJCpByF72LAKHZKD9sqXseg3wFyqiym7u2V5_hKy2phz8hFdNE_rpppcd-uKd8X9KyLHdw5nFa3MsSj-7pTnE1pQxWe03GuJXMs19Niv3S-dHLP8cjIbVVdjDDgXg8qaUgQ2vemfH570zC2QALmpUUbYOiKKSdOBxR5TN45ZvMRlzU0FCFcTEBzZk6yQGDzwSFyBLmFu-z3N7jAk7NLNK1tHg5Pj8x-n3ryBgyeCgKSejpmgkVA-8ZXSMolEGAud8JjTkAlwFlLDgENwC0IqwQC8RpB9hb5KdBhoEQYbaLGYFGoTYaF9IQ15XUxlyKhMKUlSSHa4ogBgadBB-82nzMSc3dw02cgzx8tMTIeVzL7gDvrWik4dpcffhLYbfcjmVl1mxOCp1FBIdtBuqyNv3WTffvJ_S2T9Qc_ufPl_0S30AVAbdRPdttFiNavVV0BGFd-xJvAL5WoPMg priority: 102 providerName: Wiley-Blackwell |
| Title | Numerical algorithm for solving time‐fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fnum.22209 https://www.proquest.com/docview/2078290573 https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/num.22209 |
| UnpaywallVersion | publishedVersion |
| Volume | 34 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVEBS databaseName: EBSCOhost Academic Search Ultimate customDbUrl: https://search.ebscohost.com/login.aspx?authtype=ip,shib&custid=s3936755&profile=ehost&defaultdb=asn eissn: 1098-2426 dateEnd: 20241103 omitProxy: true ssIdentifier: ssj0011519 issn: 0749-159X databaseCode: ABDBF dateStart: 20120901 isFulltext: true titleUrlDefault: https://search.ebscohost.com/direct.asp?db=asn providerName: EBSCOhost – providerCode: PRVEBS databaseName: EBSCOhost Mathematics Source - HOST customDbUrl: eissn: 1098-2426 dateEnd: 20241103 omitProxy: false ssIdentifier: ssj0011519 issn: 0749-159X databaseCode: AMVHM dateStart: 20120901 isFulltext: true titleUrlDefault: https://www.ebsco.com/products/research-databases/mathematics-source providerName: EBSCOhost – providerCode: PRVWIB databaseName: Wiley Online Library - Core collection (SURFmarket) issn: 0749-159X databaseCode: DR2 dateStart: 19960101 customDbUrl: isFulltext: true eissn: 1098-2426 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0011519 providerName: Wiley-Blackwell |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NattAEF6CfQg5NG2aUhcnLE0PvshFq7_V0YQEU7ApIQb3pO5vbarIri0RnFMeIIc8Y58ks7uSW5e2FHqSkEaLVjs78-2M9huE3rFARZwkxFM-T0zohnhMauklvs8JlQmPbK3D0TgeTsIP02ha1zk1e2EcP8Q24GZmhrXXZoIvoRFrB-rsPnlfVDd9cHBmA187jgCMt1B7Mv44-OTIN1MPnPXU5jtTapKfccMt9POzux7pB8zcr4ol29yyPN8FrtbzXB6iz807ux9OvvarkvfF3S90jv_RqefoWY1K8cCp0Qu0p4ojdDDaUrquX6KHceWSOzlm-ZfFal7ObjAgXgzKa4IS2FSp_37_qFduqwTILY1awtFRUiyaWiz2mvrmOMbXeF1xEwvC5QIE5_YmKyQGWzwXM9AqzG3lp9UGw9Jduj_MjtHk8uL6fOjVpRw8EQQk9XTMBI2E8omvlJZJJMJY6ITHnIZMgNmQGjocgoEQUgkGMBZGMw59legw0CIMXqFWsSjUa4SF9oU0NHYxlSGjMqUkSWHZwxUFKEuDDuo1w5mJmufclNvIM8fQTEytlcx-4A56uxVdOnKP3wl1G53I6vm9zohBVqkhk-ygs62e_K2Rnh32P0tk48nInrz5pwa7qFWuKnUCiKjkp7AWuCKnte4_ATxBEnk |
| linkProvider | Unpaywall |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9NAEB5V5VA48EYECqyAQy9O8XptryUuCFEFaHJAjZQLsvZJI1wnJLZQOfEDOPAb-0s6uxsbigAhTrbsseW15_HNePcbgKciMamkOY1MLHNXuqGR0FZHeRxLynUuU9_rcDzJRlP2ZpbOtuB5txYm8EP0BTdnGd5fOwN3Ben9n1hD25MhRje3eu8SyzBPcZDoXU8ehVDHt_XAGFlEGLRnHa_QM7rfX3oxGv2AmDttvRSnn0VVXQStPuocXIP33fOGySYfh20jh-rLL1SO_zug63B1A0fJi6A_N2DL1Dfhyrjncl3fgm-TNvzVqYioPixW8-b4hCDUJai1rhpBXHv6s6_f7SqskUC5pdNH3AYuikXXhMUfM58CufiarFvpikCkWaDg3J8UtSbohOfqGNWJSN_yaXVKMGfXYWrZbZgevDp6OYo2PRwilSS0iGwmFE-ViWlsjNV5qlimbC4zyZlQ6C-0xQEz9AxKGyUQv6aYgLHY5JYlVrHkDmzXi9rcBaJsrLTjr8u4ZoLrgtO8wHxHGo4YlicD2Ou-Zak2BOeuz0ZVBmpm6pqslP4FD-BxL7oMrB6_E9rtFKLcGPa6pA5SFY5FcgBPeiX52032_Df_s0Q5mY79zr1_F30EO6Oj8WF5-Hry9j5cRhDHw7y3XdhuVq15gECpkQ-9PZwDxM4TUw |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9NAEB5VReJx4I0IFFgBh16c1uu1vZa4IEpUHokQIlIuyNonjXCdkNhC5cQP4MBv5JcwuxsbigAhTrbsseW15_HtePYbgIciMamkOY1MLHOXuqGR0FZHeRxLynUuU9_rcDzJDqfs-SydbcGjbi1M4IfoE27OMry_dgZultru_cQa2h4PMbq51XtnWFpwV9B38Lonj0Ko49t6YIwsIgzas45XaJ_u9ZeejkY_IOa5tl6Kk4-iqk6DVh91Rpfgbfe8odjk_bBt5FB9-oXK8X8HdBkubuAoeRz05wpsmfoqXBj3XK7ra_Bl0oa_OhUR1bvFat4cHROEugS11mUjiGtP_-3zV7sKayRQbun0EbeBi2LRNWHxx8yHQC6-JutWuiQQaRYoOPcnRa0JOuG5OkJ1ItK3fFqdEJyz61Badh2mo6dvnhxGmx4OkUoSWkQ2E4qnysQ0NsbqPFUsUzaXmeRMKPQX2uKAGXoGpY0SiF9TnICx2OSWJVax5AZs14va3ASibKy046_LuGaC64LTvMD5jjQcMSxPBrDbfctSbQjOXZ-NqgzUzNQ1WSn9Cx7A_V50GVg9fie00ylEuTHsdUkdpCoci-QAHvRK8reb7Ppv_meJcjId-51b_y56D86-OhiVL59NXtyG84jheCh724HtZtWaO4iTGnnXm8N3VQoS1w |
| linkToUnpaywall | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT-MwELZQOSAOy_LSFrHIAg5cUhTn5RwRAiGkVhyoVE7BT6g2pKVNhNjT_gAO_EZ-CWM7KQ8BWolTomRixfF45vNM_A1CuyxQEScJ8ZTPExO6IR6TWnqJ73NCZcIjW-uw24tP-uHpIBrUdU7NXhjHDzELuJmZYe21meBjaMTagTq7T_aL6qYDDs5s4JuPIwDjLTTf750dXDjyzdQDZz2w-c6UmuRn3HALvX72rUd6gZkLVTFm93csz98CV-t5jpfQZfPO7oeTP52q5B3x9x2d4zc69RP9qFEpPnBqtIzmVLGCFrszStfpKnroVS65k2OWX40mw_L6BgPixaC8JiiBTZX6p3-PeuK2SoDc2KglHB0lxaipxWKvqVvHMT7F04qbWBAuRyA4tDdZITHY4qG4Bq3C3FZ-mtxjWLpL94fZGuofH50fnnh1KQdPBAFJPR0zQSOhfOIrpWUSiTAWOuExpyETYDakhg6HYCCEVIIBjIXRjENfJToMtAiDddQqRoX6hbDQvpCGxi6mMmRUppQkKSx7uKIAZWnQRnvNcGai5jk35TbyzDE0E1NrJbMfuI22Z6JjR-7xkdBmoxNZPb-nGTHIKjVkkm20M9OTrxrZs8P-uUTW63ftycZ_NbiJWuWkUr8BEZV8q9b6Z9NIEZA |
| 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=Numerical+algorithm+for+solving+time%E2%80%90fractional+partial+integrodifferential+equations+subject+to+initial+and+Dirichlet+boundary+conditions&rft.jtitle=Numerical+methods+for+partial+differential+equations&rft.au=Abu+Arqub%2C+Omar&rft.au=Al%E2%80%90Smadi%2C+Mohammed&rft.date=2018-09-01&rft.issn=0749-159X&rft.eissn=1098-2426&rft.volume=34&rft.issue=5&rft.spage=1577&rft.epage=1597&rft_id=info:doi/10.1002%2Fnum.22209&rft.externalDBID=10.1002%252Fnum.22209&rft.externalDocID=NUM22209 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0749-159X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0749-159X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0749-159X&client=summon |