LEADER 04439nam 22006735 450 001 9910863137003321 005 20251113190356.0 010 $a3-662-61550-9 024 7 $a10.1007/978-3-662-61550-8 035 $a(CKB)4100000011528437 035 $a(MiAaPQ)EBC6381292 035 $a(DE-He213)978-3-662-61550-8 035 $a(PPN)258059141 035 $a(EXLCZ)994100000011528437 100 $a20201027d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMittag-Leffler Functions, Related Topics and Applications /$fby Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei Rogosin 205 $a2nd ed. 2020. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2020. 215 $a1 online resource (XVI, 540 p. 22 illus., 11 illus. in color.) 225 1 $aSpringer Monographs in Mathematics,$x2196-9922 311 08$a3-662-61549-5 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction -- Overview on the Mittag-Leffler funtion -- Classical Mittag-Laffler function -- Two-parametric Mittag-Leffler functions with three parameters -- Multi-index and multi-variable Mittag-Leffler functions. - The Classical Wright function. - Applications to solution of fractional order equations. - Applications to deterministic models -- Applications to stochastic models. - Appendix A. The Eulerian functions -- Appendix B. Basic of Entire Functions -- Appendix C. Integral transforms -- Appendix D. Mellin-Barnes integral. - Appendix E. Elements of Fractional Calculus -- Appendix F. Higher transcendental functions -- References -- Index. 330 $aThe 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication of the 1st edition, but not covered there. As a result of researchers? and scientists? increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have caught the interest of the scientific community. Focusing on the theory of Mittag-Leffler functions, this volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular, the Mittag-Leffler functions make it possible to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and related special functions. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, control theory and several other related areas. 410 0$aSpringer Monographs in Mathematics,$x2196-9922 606 $aMathematical physics 606 $aSpecial functions 606 $aMathematical models 606 $aIntegral equations 606 $aProbabilities 606 $aMathematical Physics 606 $aSpecial Functions 606 $aMathematical Modeling and Industrial Mathematics 606 $aIntegral Equations 606 $aProbability Theory 615 0$aMathematical physics. 615 0$aSpecial functions. 615 0$aMathematical models. 615 0$aIntegral equations. 615 0$aProbabilities. 615 14$aMathematical Physics. 615 24$aSpecial Functions. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aIntegral Equations. 615 24$aProbability Theory. 676 $a515.75 700 $aGorenflo$b Rudolf$042618 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910863137003321 996 $aMittag-Leffler Functions, Related Topics and Applications$91749652 997 $aUNINA