| Description |
1 online resource |
| Series |
Lecture notes in mathematics, 0075-8434 ; 2056 |
|
Lecture notes in mathematics (Springer-Verlag) ; 2056.
|
| Contents |
Preliminaries -- q-Difference Equations -- q-Sturm-Liouville Problems -- Riemann-Liouville q-Fractional Calculi -- Other q-Fractional Calculi -- Fractional q-Leibniz Rule and Applications -- q-Mittag-Leffler Functions -- Fractional q-Difference Equations -- q-Integral Transforms for Solving Fractional q-Difference Equations |
| Summary |
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-Mellin-Barnes integral and Hankel contour integral representation of the q-Mittag-Leffler functions under consideration, the distribution, asymptotic and reality of their zeros, establishing q-counterparts of Wiman's results. Fractional q-difference equations are studied; existence and uniqueness theorems are given and classes of Cauchy-type problems are completely solved in terms of families of q-Mittag-Leffler functions. Among many q-analogs of classical results and concepts, q-Laplace, q-Mellin and q2-Fourier transforms are studied and their applications are investigated |
| Analysis |
Mathematics |
|
Global analysis (Mathematics) |
|
Functional equations |
|
Functions of complex variables |
|
Integral equations |
|
Integral Transforms |
|
Analysis |
|
Difference and Functional Equations |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
| Subject |
Fractional calculus.
|
|
Ecuaciones integrales
|
|
Funciones, Teoría geométrica de
|
|
Fractional calculus
|
| Form |
Electronic book
|
| Author |
Mansour, Zeinab S
|
| ISBN |
9783642308987 |
|
3642308988 |
|
364230897X |
|
9783642308970 |
|
