{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T14:42:59Z","timestamp":1744036979103},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2017,8,5]],"date-time":"2017-08-05T00:00:00Z","timestamp":1501891200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s00521-017-3163-9","type":"journal-article","created":{"date-parts":[[2017,8,5]],"date-time":"2017-08-05T01:59:16Z","timestamp":1501898356000},"page":"1867-1878","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["The construction of operational matrix of fractional integration for solving fractional differential and integro-differential equations"],"prefix":"10.1007","volume":"31","author":[{"given":"Farzane","family":"Yousefi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Azim","family":"Rivaz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,8,5]]},"reference":[{"issue":"1","key":"3163_CR1","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1122\/1.549887","volume":"30","author":"RL Bagley","year":"1986","unstructured":"Bagley RL, Torvik PJ (1986) On the fractional calculus model of viscoelastic behavior. J Rheol 30(1):133\u2013155. doi:\n                    10.1122\/1.549887","journal-title":"J Rheol"},{"issue":"10","key":"3163_CR2","doi-asserted-by":"publisher","first-page":"2803","DOI":"10.1016\/j.sigpro.2006.02.022","volume":"86","author":"AJ Calderon","year":"2006","unstructured":"Calderon AJ, Vinagre BM, Feliu V (2006) Fractional order control strategies for power electronic buck converters. Signal Process 86(10):2803\u20132819. doi:\n                    10.1016\/j.sigpro.2006.02.022","journal-title":"Signal Process"},{"key":"3163_CR3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.034101","author":"I Grigorenko","year":"2003","unstructured":"Grigorenko I, Grigorenko E (2003) Chaotic dynamics of the fractional Lorenz system. Phys Rev Lett. doi:\n                    10.1103\/PhysRevLett.91.034101","journal-title":"Phys Rev Lett"},{"issue":"4","key":"3163_CR4","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1515\/anona-2013-0033","volume":"5","author":"S Kumar","year":"2016","unstructured":"Kumar S, Kumar D, Singh J (2016) Fractional modelling arising in unidirectional propagation of long waves in dispersive media. Adv Nonlinear Anal 5(4):383\u2013394. doi:\n                    10.1515\/anona-2013-0033","journal-title":"Adv Nonlinear Anal"},{"key":"3163_CR5","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.egypro.2012.05.194","volume":"19","author":"A Al Jarbouh","year":"2012","unstructured":"Al Jarbouh A (2012) Rheological behaviour modelling of viscoelastic materials by using fractional model. Energy Procedia 19:143\u2013157. doi:\n                    10.1016\/j.egypro.2012.05.194","journal-title":"Energy Procedia"},{"key":"3163_CR6","doi-asserted-by":"crossref","unstructured":"Mainardi F (2012) Fractional calculus: some basic problems in continuum and statistical mechanics. arXiv preprint arXiv:1201.0863.\u00a0In: Carpinteri A, Mainardi F (eds) (1997)\u00a0Fractals and fractional calculus in continuum mechanics. Springer Verlag, Wien and\u00a0New York, pp 291\u2013348","DOI":"10.1007\/978-3-7091-2664-6_7"},{"issue":"6","key":"3163_CR7","doi-asserted-by":"publisher","first-page":"798","DOI":"10.1016\/j.physleta.2007.08.040","volume":"372","author":"MS Tavazoei","year":"2008","unstructured":"Tavazoei MS, Haeri M (2008) Chaos control via a simple fractional-order controller. Phys Lett A 372(6):798\u2013807. doi:\n                    10.1016\/j.physleta.2007.08.040","journal-title":"Phys Lett A"},{"issue":"1","key":"3163_CR8","doi-asserted-by":"publisher","first-page":"44","DOI":"10.2478\/s13540-012-0005-4","volume":"15","author":"A Aghajani","year":"2012","unstructured":"Aghajani A, Jalilian Y, Trujillo J (2012) On the existence of solutions of fractional integro-differential equations. Fract Calc Appl Anal 15(1):44\u201369. doi:\n                    10.2478\/s13540-012-0005-4","journal-title":"Fract Calc Appl Anal"},{"issue":"6","key":"3163_CR9","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1016\/j.aml.2010.02.007","volume":"23","author":"J Deng","year":"2010","unstructured":"Deng J, Ma L (2010) Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. Appl Math Lett 23(6):676\u2013680. doi:\n                    10.1016\/j.aml.2010.02.007","journal-title":"Appl Math Lett"},{"issue":"2","key":"3163_CR10","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1007\/s11071-016-2716-2","volume":"85","author":"S Kumar","year":"2016","unstructured":"Kumar S, Kumar A, Baleanu D (2016) Two analytical methods for time-fractional nonlinear coupled Boussinesq\u2013Burgers equations arise in propagation of shallow water waves. Nonlinear Dyn 85(2):699\u2013715. doi:\n                    10.1007\/s11071-016-2716-2","journal-title":"Nonlinear Dyn"},{"issue":"1","key":"3163_CR11","doi-asserted-by":"publisher","first-page":"476","DOI":"10.1016\/j.jmaa.2008.04.007","volume":"345","author":"M Inc","year":"2008","unstructured":"Inc M (2008) The approximate and exact solutions of the space-and time-fractional Burgers equations with initial conditions by variational iteration method. J Math Anal Appl 345(1):476\u2013484. doi:\n                    10.1016\/j.jmaa.2008.04.007","journal-title":"J Math Anal Appl"},{"issue":"4","key":"3163_CR12","doi-asserted-by":"publisher","first-page":"1295","DOI":"10.1016\/j.cnsns.2008.01.010","volume":"14","author":"SS Ray","year":"2009","unstructured":"Ray SS (2009) Analytical solution for the space fractional diffusion equation by two-step Adomian decomposition method. Commun Nonlinear Sci Numer Simul 14(4):1295\u20131306. doi:\n                    10.1016\/j.cnsns.2008.01.010","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"1","key":"3163_CR13","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.cnsns.2013.04.026","volume":"19","author":"MH Heydari","year":"2014","unstructured":"Heydari MH, Hooshmandasl MR, Mohammadi F, Cattani C (2014) Wavelets method for solving systems of nonlinear singular fractional Volterra integro-differential equations. Commun Nonlinear Sci Numer Simul 19(1):37\u201348. doi:\n                    10.1016\/j.cnsns.2013.04.026","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"3163_CR14","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1016\/j.jcp.2016.02.030","volume":"312","author":"VR Hosseini","year":"2016","unstructured":"Hosseini VR, Shivanian E, Chen W (2016) Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping. J Comput Phys 312:307\u2013332. doi:\n                    10.1016\/j.jcp.2016.02.030","journal-title":"J Comput Phys"},{"issue":"2","key":"3163_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1140\/epjp\/i2015-15033-5","volume":"130","author":"VR Hosseini","year":"2015","unstructured":"Hosseini VR, Shivanian E, Chen W (2015) Local integration of 2-D fractional telegraph equation via local radial point interpolant approximation. EPJ Plus 130(2):1\u201321. doi:\n                    10.1140\/epjp\/i2015-15033-5","journal-title":"EPJ Plus"},{"key":"3163_CR16","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.enganabound.2013.10.009","volume":"38","author":"VR Hosseini","year":"2014","unstructured":"Hosseini VR, Chen W, Avazzadeh Z (2014) Numerical solution of fractional telegraph equation by using radial basis functions. Eng Anal Bound Elem 38:31\u201339. doi:\n                    10.1016\/j.enganabound.2013.10.009","journal-title":"Eng Anal Bound Elem"},{"issue":"3","key":"3163_CR17","doi-asserted-by":"publisher","first-page":"1126","DOI":"10.1016\/j.apm.2012.03.033","volume":"37","author":"S Kazem","year":"2013","unstructured":"Kazem S (2013) An integral operational matrix based on Jacobi polynomials for solving fractional-order differential equations. Appl Math Model 37(3):1126\u20131136. doi:\n                    10.1016\/j.apm.2012.03.033","journal-title":"Appl Math Model"},{"key":"3163_CR18","doi-asserted-by":"publisher","first-page":"5463","DOI":"10.22436\/jnsa.009.09.14","volume":"9","author":"C Lia","year":"2016","unstructured":"Lia C, Kumarb A, Kumarb S, Yangc XJ (2016) On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method. J Nonlinear Sci Appl 9:5463\u20135470","journal-title":"J Nonlinear Sci Appl"},{"issue":"12","key":"3163_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1177\/1687814015620330","volume":"7","author":"XB Yin","year":"2015","unstructured":"Yin XB, Kumar S, Kumar D (2015) A modified homotopy analysis method for solution of fractional wave equations. Adv Mech Eng 7(12):1\u20138. doi:\n                    10.1177\/1687814015620330","journal-title":"Adv Mech Eng"},{"issue":"20","key":"3163_CR20","doi-asserted-by":"publisher","first-page":"8903","DOI":"10.1016\/j.apm.2013.04.019","volume":"37","author":"MH Atabakzadeh","year":"2013","unstructured":"Atabakzadeh MH, Akrami MH, Erjaee GH (2013) Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations. Appl Math Model 37(20):8903\u20138911. doi:\n                    10.1016\/j.apm.2013.04.019","journal-title":"Appl Math Model"},{"issue":"1","key":"3163_CR21","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1016\/j.amc.2006.08.122","volume":"187","author":"A Kilicman","year":"2007","unstructured":"Kilicman A, Al Zhour ZAA (2007) Kronecker operational matrices for fractional calculus and some applications. Appl Math Comput 187(1):250\u2013265. doi:\n                    10.1016\/j.amc.2006.08.122","journal-title":"Appl Math Comput"},{"issue":"24","key":"3163_CR22","doi-asserted-by":"publisher","first-page":"6038","DOI":"10.1016\/j.apm.2014.04.064","volume":"38","author":"E Keshavarz","year":"2014","unstructured":"Keshavarz E, Ordokhani Y, Razzaghi M (2014) Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations. Appl Math Model 38(24):6038\u20136051. doi:\n                    10.1016\/j.apm.2014.04.064","journal-title":"Appl Math Model"},{"issue":"5","key":"3163_CR23","doi-asserted-by":"publisher","first-page":"1203","DOI":"10.1016\/j.cnsns.2012.09.024","volume":"18","author":"L Zhu","year":"2013","unstructured":"Zhu L, Fan Q (2013) Numerical solution of nonlinear fractional-order Volterra integro-differential equations by SCW. Commun Nonlinear Sci Numer Simul 18(5):1203\u20131213. doi:\n                    10.1016\/j.cnsns.2012.09.024","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"3","key":"3163_CR24","doi-asserted-by":"publisher","first-page":"1154","DOI":"10.1016\/j.cnsns.2010.05.036","volume":"16","author":"H Saeedi","year":"2011","unstructured":"Saeedi H, Moghadam MM, Mollahasani N, Chuev GN (2011) A CAS wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order. Commun Nonlinear Sci Numer Simul 16(3):1154\u20131163. doi:\n                    10.1016\/j.cnsns.2010.05.036","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"3","key":"3163_CR25","doi-asserted-by":"publisher","first-page":"1326","DOI":"10.1016\/j.camwa.2009.07.006","volume":"59","author":"A Saadatmandi","year":"2010","unstructured":"Saadatmandi A, Dehghan M (2010) A new operational matrix for solving fractional-order differential equations. Comput Math Appl 59(3):1326\u20131336. doi:\n                    10.1016\/j.camwa.2009.07.006","journal-title":"Comput Math Appl"},{"key":"3163_CR26","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1016\/j.amc.2013.06.102","volume":"230","author":"M Yi","year":"2014","unstructured":"Yi M, Huang J (2014) Wavelet operational matrix method for solving fractional differential equations with variable coefficients. Appl Math Comput 230:383\u2013394. doi:\n                    10.1016\/j.amc.2013.06.102","journal-title":"Appl Math Comput"},{"key":"3163_CR27","volume-title":"Fractional differential equations","author":"I Podlubny","year":"1999","unstructured":"Podlubny I (1999) Fractional differential equations. Academic Press, San Diego"},{"key":"3163_CR28","volume-title":"Spectral methods in fluid dynamics","author":"C Canuto","year":"2012","unstructured":"Canuto C, Hussaini MY, Quarteroni AM, Thomas JrA (2012) Spectral methods in fluid dynamics. Springer, Berlin"},{"key":"3163_CR29","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0009162","volume-title":"Block pulse functions and their applications in control systems","author":"Z Jiang","year":"1992","unstructured":"Jiang Z, Schoufelberger W, Thoma M, Wyner A (1992) Block pulse functions and their applications in control systems. Springer, New York"},{"issue":"3","key":"3163_CR30","doi-asserted-by":"publisher","first-page":"558","DOI":"10.1002\/num.20112","volume":"22","author":"VJ Ervin","year":"2006","unstructured":"Ervin VJ, Roop JP (2006) Variational formulation for the stationary fractional advection dispersion equation. Numer Methods Partial Differ Equ 22(3):558\u2013576. doi:\n                    10.1002\/num.20112","journal-title":"Numer Methods Partial Differ Equ"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-017-3163-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-017-3163-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-017-3163-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,19]],"date-time":"2019-06-19T05:29:13Z","timestamp":1560922153000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-017-3163-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,5]]},"references-count":30,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["3163"],"URL":"https:\/\/doi.org\/10.1007\/s00521-017-3163-9","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,5]]},"assertion":[{"value":"16 July 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 July 2017","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 August 2017","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}