Author 
Annaby, Mahmoud H.

Series 
Lecture notes in mathematics, 00758434 ; 2056 

Lecture notes in mathematics (SpringerVerlag) ;
2056.

Subject 
Fractional calculus.

Alt Name 
Mansour, Zeinab S.

Description 
1 online resource. 
Contents 
Preliminaries  qDifference Equations  qSturmLiouville Problems  RiemannLiouville qFractional Calculi  Other qFractional Calculi  Fractional qLeibniz Rule and Applications  qMittagLeffler Functions  Fractional qDifference Equations  qIntegral Transforms for Solving Fractional qDifference Equations. 
Bibliography Note 
Includes bibliographical references and index. 
Summary 
This ninechapter monograph introduces a rigorous investigation of qdifference operators in standard and fractional settings. It starts with elementary calculus of qdifferences and integration of Jackson's type before turning to qdifference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular qSturmLiouville 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 qcalculi. Hence fractional qcalculi of the types RiemannLiouville; GrunwaldLetnikov; Caputo; ErdelyiKober and Weyl are defined analytically. Fractional qLeibniz rules with applications in qseries are also obtained with rigorous proofs of the formal results of AlSalamVerma, which remained unproved for decades. In working towards the investigation of qfractional difference equations; families of qMittagLeffler functions are defined and their properties are investigated, especially the qMellinBarnes integral and Hankel contour integral representation of the qMittagLeffler functions under consideration, the distribution, asymptotic and reality of their zeros, establishing qcounterparts of Wiman's results. Fractional qdifference equations are studied; existence and uniqueness theorems are given and classes of Cauchytype problems are completely solved in terms of families of qMittagLeffler functions. Among many qanalogs of classical results and concepts, qLaplace, qMellin and q2Fourier transforms are studied and their applications are investigated. 
Note 
English. 
ISBN 
9783642308987 (electronic bk.) 

3642308988 (electronic bk.) 

364230897X 

9783642308970 

9783642308970 
ISBN/ISSN 
10.1007/9783642308987 
OCLC # 
809202760 
Additional Format 
Printed edition: 9783642308970 
