LEADER 05048nam 22008055 450 001 9910299992403321 005 20200629192745.0 010 $a3-662-43930-1 024 7 $a10.1007/978-3-662-43930-2 035 $a(CKB)3710000000262070 035 $a(EBL)1967828 035 $a(OCoLC)896839826 035 $a(SSID)ssj0001372701 035 $a(PQKBManifestationID)11824363 035 $a(PQKBTitleCode)TC0001372701 035 $a(PQKBWorkID)11310890 035 $a(PQKB)10688430 035 $a(MiAaPQ)EBC1967828 035 $a(DE-He213)978-3-662-43930-2 035 $a(PPN)182098559 035 $a(EXLCZ)993710000000262070 100 $a20141016d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMittag-Leffler Functions, Related Topics and Applications /$fby Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin 205 $a1st ed. 2014. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2014. 215 $a1 online resource (454 p.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 300 $aDescription based upon print version of record. 311 $a3-662-43929-8 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction -- 1.History of Mittag-Leffler functions -- 2.Classical Mittag-Leffler function -- 3.Mittag-Leffler functions with two or three parameters -- 4.Generalized Mittag-Leffler functions -- 5.Mittag-Leffler functions and solution to fractional order equations -- 6.Applications to deterministic models -- 7.Applications to stochastic models -- Appendices -- A. Euler Gamma and Beta-functions -- B. Entire functions -- C. Integral transforms -- D. Mellin-Barnes integral -- E. Elements of fractional calculus -- F. Higher transcendental functions -- References. 330 $aAs a result of researchers? and scientists? increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have recently caught the interest of the scientific community. Focusing on the theory of the Mittag-Leffler functions, the present volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to the applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular the Mittag-Leffler functions allow us to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and its successors. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, theory of control, and several other related areas. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aSpecial functions 606 $aMathematical physics 606 $aMathematical models 606 $aIntegral equations 606 $aProbabilities 606 $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 606 $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aSpecial functions. 615 0$aMathematical physics. 615 0$aMathematical models. 615 0$aIntegral equations. 615 0$aProbabilities. 615 14$aSpecial Functions. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aIntegral Equations. 615 24$aProbability Theory and Stochastic Processes. 676 $a515.83 700 $aGorenflo$b Rudolf$4aut$4http://id.loc.gov/vocabulary/relators/aut$042618 702 $aKilbas$b Anatoly A$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMainardi$b Francesco$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRogosin$b Sergei V$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299992403321 996 $aMittag-Leffler Functions, Related Topics and Applications$91749652 997 $aUNINA