{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:40:22Z","timestamp":1740148822095,"version":"3.37.3"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2019,11,6]],"date-time":"2019-11-06T00:00:00Z","timestamp":1572998400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,6]],"date-time":"2019-11-06T00:00:00Z","timestamp":1572998400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2020,2]]},"DOI":"10.1007\/s12190-019-01302-w","type":"journal-article","created":{"date-parts":[[2019,11,6]],"date-time":"2019-11-06T18:03:12Z","timestamp":1573063392000},"page":"663-683","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Novel numerical method of the fractional cable equation"],"prefix":"10.1007","volume":"62","author":[{"given":"Y.","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8289-8277","authenticated-orcid":false,"given":"Chang-Ming","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,11,6]]},"reference":[{"key":"1302_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physa.2017.02.016","volume":"476","author":"A Atangana","year":"2017","unstructured":"Atangana, A., Gomez-Aguilar, J.F.: A new derivative with normal distribution kernel: theory, methods and applications. Physica A 476, 1\u201314 (2017)","journal-title":"Physica A"},{"key":"1302_CR2","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/j.chaos.2017.03.022","volume":"102","author":"A Atangana","year":"2017","unstructured":"Atangana, A., Gomez-Aguilar, J.F.: Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws. ChaosSolitons Fractals 102, 285\u2013294 (2017)","journal-title":"ChaosSolitons Fractals"},{"key":"1302_CR3","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1016\/j.chaos.2018.07.033","volume":"114","author":"A Atangana","year":"2018","unstructured":"Atangana, A., Gomez-Aguilar, J.F.: Fractional derivatives with no-index law property: application to chaos and statistics. Chaos Solitons Fractals 114, 516\u2013535 (2018)","journal-title":"Chaos Solitons Fractals"},{"key":"1302_CR4","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/s11071-014-1854-7","volume":"80","author":"AH Bhrawy","year":"2015","unstructured":"Bhrawy, A.H., Zaky, M.A.: Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation. Nonlinear Dyn. 80, 101\u2013116 (2015)","journal-title":"Nonlinear Dyn."},{"key":"1302_CR5","doi-asserted-by":"publisher","first-page":"886","DOI":"10.1016\/j.jcp.2007.05.012","volume":"227","author":"C-M Chen","year":"2007","unstructured":"Chen, C.-M., Liu, F., Turner, I., Anh, V.: Fourier method for the fractional diffusion equation describing sub-diffusion. J. Comput. Phys. 227, 886\u2013897 (2007)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"1302_CR6","doi-asserted-by":"publisher","first-page":"1740","DOI":"10.1137\/090771715","volume":"32","author":"C-M Chen","year":"2010","unstructured":"Chen, C.-M., Liu, F., Anh, V., Turner, I.: Numerical schemes with high spatial accuracy for a variable-order anomalous subdiffusion equation. SIAM J. Sci. Comput. 32(4), 1740\u20131760 (2010)","journal-title":"SIAM J. Sci. Comput."},{"key":"1302_CR7","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/j.cam.2011.06.019","volume":"236","author":"C-M Chen","year":"2011","unstructured":"Chen, C.-M., Liu, F., Burrage, K.: Numerical analysis for a variable-order nonlinear cable equation. J. Comput. Appl. Math. 236, 209\u2013224 (2011)","journal-title":"J. Comput. Appl. Math."},{"key":"1302_CR8","first-page":"329","volume":"238","author":"YM Chen","year":"2014","unstructured":"Chen, Y.M., Liu, L.Q., Li, B.F., Sun, Y.N.: Numerical solution for the variable order linear cable equation with Bernstein polynomials. Appl. Math. Comput. 238, 329\u2013341 (2014)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"1302_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1140\/epjp\/i2017-11293-3","volume":"132","author":"JF Gomez-Aguilar","year":"2017","unstructured":"Gomez-Aguilar, J.F., et al.: New insight in fractional differentiation: power, exponential decay and Mittag-Leffler laws and applications. Eur. Phys. J. Plus 132(1), 1\u201323 (2017)","journal-title":"Eur. Phys. J. Plus"},{"issue":"2","key":"1302_CR10","doi-asserted-by":"publisher","first-page":"55","DOI":"10.3390\/e19020055","volume":"19","author":"JF Gomez-Aguilar","year":"2017","unstructured":"Gomez-Aguilar, J.F., et al.: Bateman\u2013Feshbach Tikochinsky and Caldirola\u2013Kanai oscillators with new fractional differentiation. Entropy 19(2), 55 (2017)","journal-title":"Entropy"},{"key":"1302_CR11","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1186\/s13662-016-0908-1","volume":"2016","author":"JF Gomez-Aguilar","year":"2016","unstructured":"Gomez-Aguilar, J.F., et al.: Fractional Li\u00e9nard type model of a pipeline within the fractional derivative without singular kernel. Adv. Differ. Equ. N. Y. 2016, 173 (2016)","journal-title":"Adv. Differ. Equ. N. Y."},{"issue":"1","key":"1302_CR12","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1186\/s13662-017-1120-7","volume":"2017","author":"JF Gomez-Aguilar","year":"2017","unstructured":"Gomez-Aguilar, J.F., et al.: Homotopy perturbation transform method for nonlinear differential equations involving to fractional operator with exponential kernel. Adv. Differ. Equ. N. Y. 2017(1), 68 (2017)","journal-title":"Adv. Differ. Equ. N. Y."},{"key":"1302_CR13","doi-asserted-by":"publisher","first-page":"128103","DOI":"10.1103\/PhysRevLett.100.128103","volume":"100","author":"BI Henry","year":"2008","unstructured":"Henry, B.I., Langlands, T.A.M.: Fractional cable models for spiny neuronal dendrites. Phys. Rev. Lett. 100, 128103 (2008)","journal-title":"Phys. Rev. Lett."},{"key":"1302_CR14","doi-asserted-by":"publisher","first-page":"4027","DOI":"10.1016\/j.apm.2011.11.027","volume":"36","author":"XL Hu","year":"2012","unstructured":"Hu, X.L., Zhang, L.M.: Implicit compact difference schemes for the fractional cable equation. Appl. Math. Model. 36, 4027\u20134043 (2012)","journal-title":"Appl. Math. Model."},{"key":"1302_CR15","doi-asserted-by":"publisher","DOI":"10.1186\/1687-2770-2014-58","author":"M Inc","year":"2014","unstructured":"Inc, M., Cavlak, E., Bayram, M.: An approximate solution of fractional cable equation by homotopy analysis method. Bound. Value Probl. (2014). \nhttps:\/\/doi.org\/10.1186\/1687-2770-2014-58","journal-title":"Bound. Value Probl."},{"key":"1302_CR16","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1134\/S0965542516010103","volume":"56","author":"S Irandoust-Pakchin","year":"2016","unstructured":"Irandoust-Pakchin, S., Javidi, M., Kheiri, H.: Analytical solutions for the fractional nonlinear cable equation using a modified homotopy perturbation and separation of variables methods. Comput. Math. Math. Phys. 56, 116\u2013131 (2016)","journal-title":"Comput. Math. Math. Phys."},{"key":"1302_CR17","unstructured":"Langlands, T.A.M., Henry, B.I., Wearne, S.L.: Solution of a fractional cable equation: finite case. Applied Mathematics Report AMR05\/35, University of New South Wales (2005)"},{"key":"1302_CR18","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1007\/s00285-009-0251-1","volume":"59","author":"TAM Langlands","year":"2009","unstructured":"Langlands, T.A.M., Henry, B.I., Wearne, S.L.: Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions. J. Math. Biol. 59, 761\u2013808 (2009)","journal-title":"J. Math. Biol."},{"key":"1302_CR19","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1088\/0253-6102\/62\/1\/09","volume":"62","author":"C Li","year":"2014","unstructured":"Li, C., Deng, W.H.: Analytical solutions, moments, and their asymptotic behaviors for the time-space fractional cable equation. Commun. Theor. Phys. 62, 54\u201360 (2014)","journal-title":"Commun. Theor. Phys."},{"key":"1302_CR20","doi-asserted-by":"publisher","first-page":"1369","DOI":"10.1090\/S0025-5718-2010-02438-X","volume":"80","author":"YM Lin","year":"2011","unstructured":"Lin, Y.M., Li, X.J., Xu, C.J.: Finite difference\/spectral approximations for the fractional cable equation. Math. Comput. 80, 1369\u20131396 (2011)","journal-title":"Math. Comput."},{"key":"1302_CR21","doi-asserted-by":"publisher","DOI":"10.1115\/1.4002269","author":"F Liu","year":"2011","unstructured":"Liu, F., Yang, Q., Turner, I.: Two new implicit numerical methods for the fractional cable equation. J. Comput. Nonlinear Dyn. (2011). \nhttps:\/\/doi.org\/10.1115\/1.4002269","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"1302_CR22","doi-asserted-by":"publisher","first-page":"2535","DOI":"10.1007\/s11071-016-2843-9","volume":"85","author":"Y Liu","year":"2016","unstructured":"Liu, Y., Du, Y.W., Li, H., Wang, J.F.: A two-grid finite element approximation for a nonlinear time-fractional cable equation. Nonlinear Dyn. 85, 2535\u20132548 (2016)","journal-title":"Nonlinear Dyn."},{"issue":"1","key":"1302_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1140\/epjp\/i2017-11341-0","volume":"132","author":"VF Morales-Delgado","year":"2017","unstructured":"Morales-Delgado, V.F., et al.: On the solutions of fractional order of evolution equations. Eur. Phys. J. Plus 132(1), 1\u201317 (2017)","journal-title":"Eur. Phys. J. Plus"},{"key":"1302_CR24","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/j.chaos.2018.03.013","volume":"110","author":"E Shivanian","year":"2018","unstructured":"Shivanian, E., Jafarabadi, A.: An improved meshless algorithm for a kind of fractional cable problem with error estimate. Chaos Solitons Fractals 110, 138\u2013151 (2018)","journal-title":"Chaos Solitons Fractals"},{"issue":"22","key":"1302_CR25","doi-asserted-by":"publisher","first-page":"1850251","DOI":"10.1142\/S0217984918502512","volume":"32","author":"E Shivanian","year":"2018","unstructured":"Shivanian, E., Jafarabadi, A.: Time fractional modified anomalous sub-diffusion equation with a nonlinear source term through locally applied meshless radial point interpolation. Mod. Phys. Lett. B 32(22), 1850251 (2018)","journal-title":"Mod. Phys. Lett. B"},{"key":"1302_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.apnum.2018.02.008","volume":"129","author":"E Shivanian","year":"2018","unstructured":"Shivanian, E., Jafarabadi, A.: The spectral meshless radial point interpolation method for solving an inverse source problem of the time-fractional diffusion equation. Appl. Numer. Math. 129, 1\u201325 (2018)","journal-title":"Appl. Numer. Math."},{"key":"1302_CR27","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.cam.2017.11.046","volume":"336","author":"E Shivanian","year":"2018","unstructured":"Shivanian, E., Jafarabadi, A.: Analysis of the spectral meshless radial point interpolation for solving fractional reaction-subdiffusion equation. J. Comput. Appl. Math. 336, 98\u2013113 (2018)","journal-title":"J. Comput. Appl. Math."},{"key":"1302_CR28","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1140\/epjp\/i2016-16061-3","volume":"131","author":"YZ Wang","year":"2016","unstructured":"Wang, Y.Z., Liu, Y., Li, H., Wang, J.F.: Finite element method combined with second-order time discrete scheme for nonlinear fractional cable equation. Eur. Phys. J. Plus 131, 61 (2016). \nhttps:\/\/doi.org\/10.1140\/epjp\/i2016-16061-3","journal-title":"Eur. Phys. J. Plus"},{"issue":"4","key":"1302_CR29","first-page":"310","volume":"62","author":"H Yepez-Martinez","year":"2016","unstructured":"Yepez-Martinez, H., et al.: The Feng\u2019s first integral method applied to the nonlinear mKdV space-time fractional partial differential equation. Rev. Mex. Fs. 62(4), 310\u2013316 (2016)","journal-title":"Rev. Mex. Fs."},{"key":"1302_CR30","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1007\/s10915-015-0136-y","volume":"68","author":"B Yu","year":"2016","unstructured":"Yu, B., Jiang, X.Y.: Numerical identification of the fractional derivatives in the two-dimensional fractional cable equation. J. Sci. Comput. 68, 252\u2013272 (2016)","journal-title":"J. Sci. Comput."},{"key":"1302_CR31","doi-asserted-by":"publisher","first-page":"1710","DOI":"10.1016\/j.camwa.2014.10.019","volume":"68","author":"HX Zhang","year":"2014","unstructured":"Zhang, H.X., Yang, X.H., Han, X.L.: Discrete-time orthogonal spline collocation method with application to two-dimensional fractional cable equation. Comput. Math. Appl. 68, 1710\u20131722 (2014)","journal-title":"Comput. Math. Appl."},{"key":"1302_CR32","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1007\/s11075-015-0055-x","volume":"72","author":"P Zhuang","year":"2016","unstructured":"Zhuang, P., Liu, F., Turner, I., Anh, V.: Galerkin finite element method and error analysis for the fractional cable equation. Numer. Algorithms 72, 447\u2013466 (2016)","journal-title":"Numer. Algorithms"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-019-01302-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12190-019-01302-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-019-01302-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,5]],"date-time":"2020-11-05T00:39:28Z","timestamp":1604536768000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12190-019-01302-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,6]]},"references-count":32,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2020,2]]}},"alternative-id":["1302"],"URL":"https:\/\/doi.org\/10.1007\/s12190-019-01302-w","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"type":"print","value":"1598-5865"},{"type":"electronic","value":"1865-2085"}],"subject":[],"published":{"date-parts":[[2019,11,6]]},"assertion":[{"value":"22 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 November 2019","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}