{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T14:07:18Z","timestamp":1742911638710,"version":"3.40.3"},"publisher-location":"Cham","reference-count":32,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319098999"},{"type":"electronic","value":"9783319099002"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-09900-2_22","type":"book-chapter","created":{"date-parts":[[2014,8,16]],"date-time":"2014-08-16T10:10:19Z","timestamp":1408183819000},"page":"239-247","source":"Crossref","is-referenced-by-count":7,"title":["Reconstruction of the Thermal Conductivity Coefficient in the Time Fractional Diffusion Equation"],"prefix":"10.1007","author":[{"given":"Rafa\u0142","family":"Brociek","sequence":"first","affiliation":[]},{"given":"Damian","family":"S\u0142ota","sequence":"additional","affiliation":[]},{"given":"Roman","family":"Witu\u0142a","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"22_CR1","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1080\/17415970902884136","volume":"17","author":"M. Ardakani","year":"2009","unstructured":"Ardakani, M., Khodadad, M.: Identification of thermal conductivity and the shape of an inclusion using the boundary elements method and the particle swarm optimization algorithm. Inverse Probl. Sci. Eng.\u00a017, 855\u2013870 (2009)","journal-title":"Inverse Probl. Sci. Eng."},{"key":"22_CR2","doi-asserted-by":"publisher","first-page":"2671","DOI":"10.1016\/S0017-9310(00)00310-0","volume":"44","author":"J.L. Battaglia","year":"2001","unstructured":"Battaglia, J.L., Cois, O., Puigsegur, L., Oustaloup, A.: Solving an inverse heat conduction problem using a\u00a0non-integer identified model. Int. J. Heat Mass Transfer\u00a044, 2671\u20132680 (2001)","journal-title":"Int. J. Heat Mass Transfer"},{"key":"22_CR3","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1016\/j.ijheatmasstransfer.2008.01.043","volume":"52","author":"V.T. Borukhov","year":"2009","unstructured":"Borukhov, V.T., Tsurko, V.A., Zayats, G.M.: The functional identification approach for numerical reconstruction of the temperature-dependent thermal-conductivity coefficient. Int. J. Heat Mass Transfer\u00a052, 232\u2013238 (2009)","journal-title":"Int. J. Heat Mass Transfer"},{"key":"22_CR4","unstructured":"Brociek, R.: Implicite finite difference metod for time fractional diffusion equations with mixed boundary conditions. Zesz. Nauk. P\u015a., Mat. Stosow. 4 (in press 2014)"},{"key":"22_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-2664-6","volume-title":"Fractal and Fractional Calculus in Continuum Mechanics","author":"A. Carpinteri","year":"1997","unstructured":"Carpinteri, A., Mainardi, F.: Fractal and Fractional Calculus in Continuum Mechanics. Springer, New York (1997)"},{"key":"22_CR6","doi-asserted-by":"publisher","first-page":"830","DOI":"10.1080\/01457630802053892","volume":"29","author":"C.L. Chang","year":"2008","unstructured":"Chang, C.L., Chang, M.: Inverse estimation of the thermal conductivity in a one-dimensional domain by Taylor series approach. Heat Transfer Engineering\u00a029, 830\u2013838 (2008)","journal-title":"Heat Transfer Engineering"},{"key":"22_CR7","doi-asserted-by":"publisher","first-page":"4254","DOI":"10.1016\/j.ijheatmasstransfer.2012.03.067","volume":"55","author":"B. Cz\u00e9l","year":"2012","unstructured":"Cz\u00e9l, B., Gr\u00f3f, G.: Inverse identification of temperature-dependent thermal conductivity via genetic algorithm with cost function-based rearrangement of genes. Int. J. Heat Mass Transfer\u00a055, 4254\u20134263 (2012)","journal-title":"Int. J. Heat Mass Transfer"},{"key":"22_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14574-2","volume-title":"The Analysis of Fractional Differential Equations","author":"K. Diethelm","year":"2010","unstructured":"Diethelm, K.: The Analysis of Fractional Differential Equations. Springer, Berlin (2010)"},{"issue":"37","key":"22_CR9","first-page":"845","volume":"A","author":"E. Divo","year":"2000","unstructured":"Divo, E., Kassab, A., Rodriguez, F.: Characterization of space dependent thermal conductivity with a\u00a0BEM-based genetic algorithm. Numer. Heat Transfer\u00a0A(37), 845\u2013875 (2000)","journal-title":"Numer. Heat Transfer"},{"key":"22_CR10","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/j.enganabound.2013.12.001","volume":"40","author":"F. Dou","year":"2014","unstructured":"Dou, F., Hon, Y.: Numerical computation for backward time-fractional diffusion equation. Eng. Anal. Bound. Elem.\u00a040, 138\u2013146 (2014)","journal-title":"Eng. Anal. Bound. Elem."},{"key":"22_CR11","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1016\/j.sigpro.2010.02.005","volume":"91","author":"J.D. Gabano","year":"2011","unstructured":"Gabano, J.D., Poinot, T.: Fractional modelling and identification of thermal systems. Signal Processing\u00a091, 531\u2013541 (2011)","journal-title":"Signal Processing"},{"key":"22_CR12","doi-asserted-by":"publisher","first-page":"938","DOI":"10.1016\/j.sigpro.2010.09.013","volume":"91","author":"J.D. Gabano","year":"2011","unstructured":"Gabano, J.D., Poinot, T.: Estimation of thermal parameters using fractional modelling. Signal Processing\u00a091, 938\u2013948 (2011)","journal-title":"Signal Processing"},{"key":"22_CR13","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1080\/17415970600844242","volume":"14","author":"A. Imani","year":"2006","unstructured":"Imani, A., Ranjbar, A.A., Esmkhani, M.: Simultaneous estimation of temperature-dependent thermal conductivity and heat capacity based on modified genetic algorithm. Inverse Probl. Sci. Eng.\u00a014, 767\u2013783 (2006)","journal-title":"Inverse Probl. Sci. Eng."},{"key":"22_CR14","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1080\/17415977.2011.629093","volume":"20","author":"F. Kanca","year":"2012","unstructured":"Kanca, F., Ismailov, M.: The inverse problem of finding the time-dependent diffusion coefficient of the heat equation from integral overdetermination data. Inverse Probl. Sci. Eng.\u00a020, 463\u2013476 (2012)","journal-title":"Inverse Probl. Sci. Eng."},{"key":"22_CR15","series-title":"Resent advances","volume-title":"Fractional dynamics","author":"J. Klafter","year":"2012","unstructured":"Klafter, J., Lim, S., Metzler, R.: Fractional dynamics. Resent advances. World Scientific, New Jersey (2012)"},{"key":"22_CR16","unstructured":"Kusiak, J., Danielewska-Tu\u0142ecka, A., Oprocha, P.: Optimization. PWN, Warszawa (2009) (in Polish)"},{"key":"22_CR17","doi-asserted-by":"publisher","first-page":"1544","DOI":"10.1016\/j.jmatprotec.2005.02.021","volume":"164-165","author":"E. Majchrzak","year":"2008","unstructured":"Majchrzak, E., Mendakiewicz, J., Piasecka-Belkhayat, A.: Algorithm of the mould thermal parameters identification in the system casting\u2013mould\u2013environment. J. Mater. Proc. Tech.\u00a0164-165, 1544\u20131549 (2008)","journal-title":"J. Mater. Proc. Tech."},{"key":"22_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-00933-9","volume-title":"Advances in the Theory and Applications of Non-integer Order Systems","author":"W. Mitkowski","year":"2013","unstructured":"Mitkowski, W., Kacprzyk, J., Baranowski, J.: Advances in the Theory and Applications of Non-integer Order Systems. Springer Inter. Publ., Cham (2013)"},{"key":"22_CR19","doi-asserted-by":"publisher","first-page":"331","DOI":"10.4028\/www.scientific.net\/SSP.180.331","volume":"180","author":"W. Mitkowski","year":"2012","unstructured":"Mitkowski, W., Obr\u0105czka, A.: Simple identification of fractional differential equation. Solid State Phenomena\u00a0180, 331\u2013338 (2012)","journal-title":"Solid State Phenomena"},{"key":"22_CR20","doi-asserted-by":"publisher","first-page":"1492","DOI":"10.1016\/j.camwa.2006.05.027","volume":"53","author":"D.A. Murio","year":"2007","unstructured":"Murio, D.A.: Stable numerical solution of a\u00a0fractional-diffusion inverse heat conduction problem. Comput. Math. Appl.\u00a053, 1492\u20131501 (2007)","journal-title":"Comput. Math. Appl."},{"key":"22_CR21","doi-asserted-by":"publisher","first-page":"1138","DOI":"10.1016\/j.camwa.2008.02.015","volume":"56","author":"D. Murio","year":"2008","unstructured":"Murio, D.: Implicit finite difference approximation for time fractional diffusion equations. Comput. Math. Appl.\u00a056, 1138\u20131145 (2008)","journal-title":"Comput. Math. Appl."},{"key":"22_CR22","doi-asserted-by":"publisher","first-page":"2371","DOI":"10.1016\/j.camwa.2008.05.015","volume":"56","author":"D. Murio","year":"2008","unstructured":"Murio, D.: Time fractional IHCP with Caputo fractional derivatives. Comput. Math. Appl.\u00a056, 2371\u20132381 (2008)","journal-title":"Comput. Math. Appl."},{"key":"22_CR23","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1080\/17415970802082872","volume":"17","author":"D. Murio","year":"2009","unstructured":"Murio, D.: Stable numerical evaluation of Gr\u00fcnwald-Letnikov fractional derivatives applied to a\u00a0fractional IHCP. Inverse Probl. Sci. Eng.\u00a017, 229\u2013243 (2009)","journal-title":"Inverse Probl. Sci. Eng."},{"key":"22_CR24","doi-asserted-by":"publisher","first-page":"12074","DOI":"10.1088\/1742-6596\/135\/1\/012074","volume":"135","author":"D. Murio","year":"2008","unstructured":"Murio, D., Mejia, C.: Generalized time fractional IHCP with Caputo fractional derivatives. J. Phys. Conf. Ser.\u00a0135, 12074 (2008)","journal-title":"J. Phys. Conf. Ser."},{"key":"22_CR25","unstructured":"Obr\u0105czka, A., Kowalski, J.: Modeling of the heat distribution in ceramic materials by using the fractional differential equations. In: Szczygie\u0142, M. (ed.) Proceedings of the XV Jubilee Symposium, Basic Problems in Power Electronics, Electromechanics and Mechatronics, PPEEm 2012, Gliwice, pp. 132\u2013133 (2012) (in Polish)"},{"key":"22_CR26","doi-asserted-by":"publisher","first-page":"265","DOI":"10.4028\/www.scientific.net\/SSP.210.265","volume":"210","author":"A. Obr\u0105czka","year":"2014","unstructured":"Obr\u0105czka, A., Mitkowski, W.: The comparison of parameter identification methods for fractional partial differential equation. Solid State Phenomena\u00a0210, 265\u2013270 (2014)","journal-title":"Solid State Phenomena"},{"key":"22_CR27","doi-asserted-by":"publisher","first-page":"3973","DOI":"10.1016\/S0017-9310(01)00025-4","volume":"44","author":"S. Orain","year":"2001","unstructured":"Orain, S., Scudeller, Y., Garcia, S., Brousse, T.: Use of genetic algorithms for the simultaneous estimation of thin film thermal conductivity and contact resistances. Int. J. Heat Mass Transfer\u00a044, 3973\u20133984 (2001)","journal-title":"Int. J. Heat Mass Transfer"},{"key":"22_CR28","volume-title":"Fractional Differential Equations","author":"I. Podlubny","year":"1999","unstructured":"Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)"},{"key":"22_CR29","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/s11071-004-3751-y","volume":"38","author":"T. Poinot","year":"2004","unstructured":"Poinot, T., Trigeassou, J.C.: Identification of fractional systems using an output-error technique. Nonlinear Dynamics\u00a038, 133\u2013154 (2004)","journal-title":"Nonlinear Dynamics"},{"key":"22_CR30","unstructured":"Rabsztyn, S., S\u0142ota, D., Witu\u0142a, R.: Gamma and Beta Functions, vol.\u00a01. Wyd. Pol. \u015al, Gliwice (2012) (in Polish)"},{"key":"22_CR31","unstructured":"Szczygie\u0142, I.: Analysis of Inverse Heat Convection Problems. Zesz. Nauk. P\u015a., Ener.\u00a0140, 1\u2013141 (2005) (in Polish)"},{"key":"22_CR32","doi-asserted-by":"publisher","first-page":"926","DOI":"10.1016\/j.automatica.2013.01.026","volume":"49","author":"S. Victor","year":"2013","unstructured":"Victor, S., Malti, R., Garnier, H., Oustaloup, A.: Parameter and differentiation order estimation in fractional models. Automatica\u00a049, 926\u2013935 (2013)","journal-title":"Automatica"}],"container-title":["Lecture Notes in Electrical Engineering","Advances in Modelling and Control of Non-integer-Order Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-09900-2_22","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T22:14:56Z","timestamp":1674166496000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-09900-2_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319098999","9783319099002"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-09900-2_22","relation":{},"ISSN":["1876-1100","1876-1119"],"issn-type":[{"type":"print","value":"1876-1100"},{"type":"electronic","value":"1876-1119"}],"subject":[],"published":{"date-parts":[[2015]]}}}