书目名称 | q-Fractional Calculus and Equations |
编辑 | Mahmoud H. Annaby,Zeinab S. Mansour |
视频video | |
概述 | First detailed rigorous study of q-calculi.First detailed rigorous study of q-difference equations.First detailed rigorous study of q-fractional calculi and equations.Proofs of many classical unproved |
丛书名称 | Lecture Notes in Mathematics |
图书封面 |  |
描述 | .This nine-chapter monograph introduces a rigorous investigation of .q-.difference operators in standard and fractional settings. It starts with elementary calculus of .q-.differences and integration of Jackson’s type before turning to .q-.difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular .q-.Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional .q.-calculi. Hence fractional .q-.calculi of the types Riemann–Liouville; Grünwald–Letnikov; Caputo; Erdélyi–Kober and Weyl are defined analytically. Fractional .q-.Leibniz rules with applications in .q-.series are also obtained with rigorous proofs of the formal results of Al-Salam-Verma, which remained unproved for decades. In working towards the investigation of .q-.fractional difference equations; families of .q-.Mittag-Leffler functions are defined and their properties are investigated, especially the .q-.Melli |
出版日期 | Book 2012 |
关键词 | 33D15, 26A33, 30C15, 39A13, 39A70; Basic Hypergeometric functions; One variable calculus; Zeros of anal |
版次 | 1 |
doi | https://doi.org/10.1007/978-3-642-30898-7 |
isbn_softcover | 978-3-642-30897-0 |
isbn_ebook | 978-3-642-30898-7Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
issn_series | 0075-8434 |
copyright | Springer-Verlag Berlin Heidelberg 2012 |